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Dott. Decio Levi

Struttura: Dip. Mat e Fis.
Ruolo: Professore Associato
SSD: FIS02
Mansione:
Mansioni Esterne:
Gruppi di Ricerca: Fisica Matematica: Sistemi non Lineari Integrabili;
Corsi del CD: Teorie dei Gruppi e Simmetrie, Fisica dei Sistemi non Lineari: caos e regolarità, Complementi di Metodi matematici della Fisica
Orario Ricevimento
Email: levi|At| roma3.infn.it
Home Page-> pagina web personale
Telefono: (+39) 065733 7034
Fax: (+39) 0657337102
Edificio: Via della Vasca Navale 84
Piano: P
Stanza: 115


Curriculum



UNIVERSITA’ DEGLI STUDI

ROMA TRE







Dipartimento di Matematica e Fisica



Via della Vasca Navale, 84

00146 Roma Italy

Fax: +390657337101

Tel: +390657337034

e-mail: levi@roma3.infn.it

Curriculum of Decio Levi



Born in Milano (Italy) on August, 9th 1948

Married with Irene Kajon with two children, Giorgina and Eugenio

Got his Laurea in Physics in 1972 with a thesis on "Computation of bound state energy for nuclei and nuclear matter with One-Boson-Exchange Potentials" directed by Prof. Francesco Calogero at the University of Rome "La Sapienza".

Postdoctoral positions in Mexico at UNAM with M. Moshinsky, in New York at the Rockfeller University with K. Case and in Rome with F. Calogero.

In 1981 he got a research position at the University of Rome "La Sapienza".

In 1988 he won a position of Associate Professor at the University of Rome "La Sapienza" in Mathematical Methods for Physicist.

From 1991 he is Associate Professor at the University Roma Tre.

From 2004 he teaches Group theory for physicists (6 credits), Symmetries and Integrability (6 credits) and Nonlinear systems in physics (5 credits) in the framework of the Master in Physics. From 2009 he teaches also Analysis (14 credits) for the degree in Optics and Optometrics.

From 2005 he is associated member of the Centre de recherches mathématiques, Université de Montréal, Montreal, Quebec, Canada.

From the academic year 2011-2012 the title of his courses in the Master in Physics changed to Group Theory and Symmetries (6 credits) and Nonlinear systems in physics: Chaos and regularity (8 credits).

From 2013 he is a member of the Dipartimento di Matematica e Fisica of Roma Tre University.





Collaborations



C.R.M. Universite' de Montreal, Montreal, Quebec, Canada - Prof. P. Winternitz, Prof. M.A. Grundland and Prof. L. Vinet.



Departamento de Fisica Teorica, Universidad Complutense, Madrid, Spain - Prof. M.A. Rodriguez and Prof. P. Tempesta.



Departimento de Matemática Aplicada a la I.T. de Telecomunicación, Escuela Universitaria de Ingeniería Técnica de Telecomunicación , Universidad Politécnica de Madrid, Spain, -Prof. Rafael Hernandez Heredero.



Institute of Theoretical Physics, University of Warsaw, Warsaw, Poland - Prof. A. Sym.



L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Chernigalovska, Moscow, Russia – Prof. S.V. Manakov and Prof. A.B. Shabat.



Ente Nazionale Energie Alternative, Casaccia, Roma, Italy - Dr. V. Artale and Dr. G. Dattoli.



Department of Physics, University of Rome III, Rome, Italy - Prof. O. Ragnisco.



Department of Physics, University of Lecce, Lecce, Italy – Prof. L. Martina.



Department of Physics, University of Rome "La Sapienza", Rome, Italy - Prof. A. Tenenbaum, Dr. A. Giansanti, Prof. P.M. Santini and Prof. M. Mattioli.



Departamento de Física Teórica, Atómica, Molecular y Nuclear, University of Valladolid, Spain - Prof. Mariano del Olmo and Prof. Javier Negro.



School of Mathematics and Statistical Sciences, La Trobe University, Melbourne, Australia – Prof. R. Quispel.



Department of Applied Mathematics, University of New South Wales, Australia - Prof. C. Rogers.



Institute of Mathematics, Russian Academy of Sciences, Ufa, Russia - Dr. R. Yamilov.



Institute of Computational Mathematics,Chinese Academy of Sciences (CAS), CHINA – Prof. Xing-Biao Hu, Dr. Gegenhasi.



Department of Mathematics, China Mining and Technology University, Beijing, Prof. Qing-Ping Liu.





Explanation of Research Contribution



His research contributions are concentrated in two separate but not completely disjoint directions: integrable systems, mainly on the lattice, and their properties and applications and symmetries of differential and difference equations.



In the first field his main results are:



Construction of integrable equations on the lattice.

Construction of a multiple scale reduction technique which reduce nonlinear equations on a lattice to nonlinear equations on the lattice, possibly integrable.

Construction of discrete integrable systems through the use of Bäcklund transformation.

Construction of Bäcklund transformations for classes of not asymptotically bounded potentials.

Applications of integrable models to physics of fluids, systems defined on a lattice and free electron lasers.



In the second field his main results are:



The construction and use of Lie point symmetries for obtaining solutions of differential equations.

The use of non-classical symmetry for the eduction for nonlinear partial differential and difference equations.

The construction of an algorithmic procedure to get classes of continuous symmetries for differential and difference equations on a lattice.

Characterization of symmetries for nonlinear differential difference equations.

Discretization through symmetries for partial differential and ordinary differential equations.

Linearization of difference equations by functional techniques and symmetries.

Classification of linearizable discrete equations defined on a lattice of three and four points.

The applications of Lie point symmetries to solve important physical and engineering problems: the Raman scattering equations, rotating shallow water in a rigid container, neo-Hookean systems, the nonrelativistic Cern-Simons equations.



Contributions to the Training of Highly Qualified Personnel



Supervision of post-docs researchers:



Dr. Vincenzo Artale on Integrable systems and Nonlinear Water Waves in Physical Media.



Dr. Ji Xiao-da on Symmetries with Personal Computer and Nonlinear Differential Equations of Interest in Applications.



Dr. Piergiulio Tempesta on Discrete Quantum Mechanics and generalized Umbral calculus.

Dr. Christian Scimiterna on analysis of difference equations: linearization and multiple scale expansions

Dr. Mike Christian Hay on hierarchies of difference equations and fake Lax pairs.



Supervision of graduate students:



D. David (1987) co-supervision Thesis on "Kadomtsev-Petviashvili type differential systems; their symmetries and an application to solitary wave propagation in non-uniform channels".

G.R. de Riencourt (1990) Thesis on "Special solutions of the cylindrical Boussinesq equation."

R. Cocci Grifoni (1991) Thesis on "Derivation of a 2+1 dimensional Boussinesq equation for an ideal fluid."

L. Mannelli (2000) Thesis on "Study of the symmetries of a class of discrete nonlinear Schrödinger equation”.

S. Tremblay (2001): co-supervision Ph-d thesis on "Symmetries of Discrete Equations"

R. Minardi (2003): Thesis on: “Propagazione solitonica in un laser ad elettroni liberi”.

S. Spampinati (2005): Thesis on: “Analisi della propagazone degli impulsi in regime di onda solitaria in un laser ad elettroni liberi”.

G. Cassatella (2007): Thesis on: “Riduzione a molte-scale sul reticolo di una catena diatomica”.

C. Scimiterna (2009) PhD Thesis on: “Multiscale techniques for nonlinear difference equations“

E. Ricca (2012): Master Thesis on: “Classification of discrete generalized Krichever-Novikov equations”.







Other Contributions.





In the development of the University of Roma Tre, which started to operate on November 1st., 1992 as a splitting of the University of Rome "La Sapienza", he was in charge for the development of the Library of the Department of Physics, member of the Faculty of Science's Committee for the development of the Faculty Libraries and representative of the Faculty of Science in the University Library Committee. In 1997-1998 he was Delegate of the Rector for the Librarian System of the University. He is Scientific Responsible for the Documentation and Information System of the University of Roma Tre and from 1999 to 2003 Coordinator of CIBER (Coordinamento InterUniversitario BasiDati ed Editoria in Rete), a Consortium between the University of Bari, Basilicata, Calabria, Campus Biomedico of Rome, Camerino, Cassino, Foggia, “G. D’Annunzio” di Chieti-Pescara, L’Aquila, Lecce, LUMSA, Macerata, Mediterranea di Reggio Calabria, Messina, Molise, Napoli II, Napoli “Partenope”, Palermo, Perugia, Roma "La Sapienza", Roma “Tor Vergata”, Roma Tre, Salerno, Tuscia and the Politechnic University of Bari. As coordinator of CIBER he was responsible for the construction of a Virtual Library, which now distribute almost 4000 periodicals on line. From 2003 he is member of the Segretary of CIBER.

He spent the months of October 1993 and August-September 2002 in China as a Visiting Scholar in the Consultant Programme of the I.C.T.P.. During that period he visited mainly Bejing, Shanghai and Hefei and gave there a sequence of lectures. Later he visited for long periods the University of Zhengzhou, the Chinese Academy of Science in Beijing, the China University of Mining and Technology in Beijing, the Tsinghua University in Beijing, sometimes times giving PhD courses on Simmetry and Integrability of Differential and Difference equations.

During his sabbatical leave from the University Roma Tre in the academic year 2002/2003 he has been for 3 months guest of the Department of Theoretical Physics II of the Universidad Complutense in Madrid, with a fellowship of the Spanish Ministry of Education and Research.

He has been Project Co-ordinator of a Nato Grant on Lie Groups and Nonlinear Integrable Differential Equations from 1987 to 1992.

He is member of the Instituto Nazionale di Fisica Nucleare, Roma Tre Section and, as part of the SPARC collaboration with Prof. M. Mattioli, also of the Sezione Roma “La Sapienza”.

He is member of the Gruppo Nazionale di Fisica Matematica of INdAM and responsible of the project on “Sistemi dinamici nonlineari discreti: simmetrie ed integrabilità”; partecipate to the project “Simmetria e riduzione di equazioni differenziali di interesse fisico-matematico”.

He is member of the American Geophysical Union.

He is member of the Unione Matematica Italiana.

He is member of he Advisory Board of SIDE (Symmetries and Integrability of Discrete Equations) Meetings.

From 2004 to 2009 he is member of the Department of Electronic Engineering and in charge of their Library.

From 2004 he is Associate Member of the Centre de Research Mathematiques of the Universite de Montreal.

From September 2004 to 2009 he is representative of Roma Tre University inside the technical committee of CASPUR (Consorzio interuniversitario per le Applicazioni di Supercalcolo Per Universita’ e Ricerca).

From April 2005 to 2009 he is co-editor of the European Physics Letters and from 2009 to 2012 member of its Advisory Board.

He is member of the Advisory Board of the Journal of Physics A.

From 2009 he is representative of Roma Tre in the Ciber Committee.

From 2010 to 2011 he is representative of Ciber in the CARE (Coordinamento per l’Accesso alle Risorse Elettroniche) Committee of the CRUI (Conferenza dei Rettori delle Universita' italiane)



Organization of International Workshops



Second Workshop on Nonlinear Evolution Equations and Dynamical Systems, The Orthodox Academy, Kolymbari near Chania, Crete; August 13-28, 1983 with F. Calogero and A. Verganelakis.



International School on Applied Mathematics: Symmetries and Nonlinear Phenomena, Paipa (Colombia); February 22-26, 1988 with P. Winternitz.



Fifth Workshop on Nonlinear Evolution Equations and Dynamical Systems, The Orthodox Academy, Kolymbari near Chania, Crete; July 2-16, 1989 with F. Calogero and A. Verganelakis.



NATO Advanced Research Workshop on Painleve' Transcendents, their asymptotics and physical applications, Sainte Adele near Montreal, Canada; September 2-7, 1990 with P. Winternitz.



Workshop on Self-Similarity in Stimulated Raman Scattering, Montreal, Canada; Marzo 1993 con C.R. Menyuk e P. Winternitz.



Symmetries and Integrability of Difference Equations (SIDE I), Esterel near Montreal, Canada; 1994 with P. Winternitz and L. Vinet



Symmetries and Integrability of Difference Equations (SIDE III), Sabaudia near Rome, Italy; May 16-22, 1998 with O. Ragnisco



AARMS-CRM Workshop on Bäcklund & Darboux Transformations: The Geometry of Soliton Theory, Halifax, Canada; June 4-9, 1999 with P. Winternitz, C. Rogers, A. Cooley and R. Milson.



Group Theory and Numerical Analysis, Montreal, Canada; 26-31 maggio 2003 con P. Winternitz, P. Olver, A. Iserles, R. Quispel.



Advanced Study Institute on Symmetry and integrability of difference equations, Montréal, Canada, June 9-21, 2008 with P. Winternitz, V. A. Dorodnitsyn, P. Olver, V. Hussin, F. Lalonde.



Symmetries and Integrability of Difference Equations (SIDE VIII), June 23-29, 2008 Mont-Gabriel near Montreal, Canada; with P. Winternitz, J.Harnad , V.Hussin, P.Olver and L. Vinet. List of Publications



Publications in refereed journals





1 One-boson-exchange potentials and nuclear structure, Physical Review C8 (1973) pp.83-92, in collaboration with F. Calogero

2 Relations between the hyper-spherical harmonic and the harmonic oscillator methods for the three body problem, Revista Mexicana de Fisica 22(1973) pp.291-319, in collaboration with E. Chacon and M. Moshinsky.

3 Relations between hyper-spherical and harmonic-oscillator many-body matrix elements, Il Nuovo Cimento A20 (1974) pp.107-114, in collaboration with M. Moshinsky.

4 Closed form of the second virial coefficient for Sutherland potential, Journal of Chemical Physics 63 (1975) pp.4561-4562, in collaboration with M. de Llano.

5 Equivalence of a class of Wigner coefficients of SU(1,1) with those of SU(2), Journal of Mathematical Physics 16 (1975) pp.1876-1879, in collaboration with E. Chacon and M. Moshinsky.

6 Generalized Van der Waals theory, Revista Mexicana de Fisica 25 (1976) pp.61-67, in collaboration with M. de Llano.

7 La mecanica cuantica y sus interpretaciones, Revista Mexicana de Fisica 25(1976) pp.E31-E62, in collaboration with T.A. Brody et.al..

8 Lie algebras in the Schrödinger picture and radial matrix elements, Journal of Mathematical Physics 17 (1976) pp.1919-1929, in collaboration with E. Chacon e M. Moshinsky.

9 Perturbative approach to some one-dimensional many-body problems I: discussion of the Rayleigh-Schrödinger and Brillouin-Wigner series for the Sutherland model, Il Nuovo Cimento B34 (1976) pp.391-410, in collaboration with O. Ragnisco.

10 Perturbative approach to some one-dimensional many-body problems. II: Brueckner approach to the Sutherland model, Il Nuovo Cimento B41 (1977) pp.137-150, in collaboration with O. Ragnisco.

11 Nonlinear evolution equations solvable by the inverse spectral transform associated to the matrix Schroedinger equation of rank 4, Il Nuovo Cimento B43 (1978) pp.251-270, in collaboration with M. Bruschi and O. Ragnisco.

12 Evolution equations associated to the triangular matrix Schrödinger problem solvable by the inverse spectral transform, Il Nuovo Cimento A45 (1978) pp.225-237, in collaboration with M. Bruschi and O. Ragnisco.

13 Extension of the spectral transform method for solving nonlinear differential difference equations, Lettere al Nuovo Cimento 22 (1978) pp.691-696, in collaboration with O. Ragnisco.

14 Discrete version of the modified Korteweg-de Vries equation with x-dependent coefficients, Il Nuovo Cimento A48 (1978) pp.213-226, in collaboration with M. Bruschi and O. Ragnisco.

15 Nonlinear differential difference equations with n-dependent coefficients I, Journal of Physics A: Math.Gen. 12 (1979) pp. L157-L162, in collaboration with O. Ragnisco.

16 Nonlinear differential difference equations with n-dependent II, Journal of Physics A: Math.Gen. 12 (1979) pp.L163-L167, in collaboration with O. Ragnisco.

17 Discrete version of the nonlinear Schrödinger equation with linearly x-dependent coefficients, Il Nuovo Cimento A53 (1979) pp.21-30, in collaboration with M. Bruschi and O. Ragnisco.

18 Toda lattice and generalized wronskian technique, Journal of Physics A:Math.Gen. 13 (1980) pp.2531-2533, in collaboration with M. Bruschi and O. Ragnisco.

19 Group theoretical approach to nonlinear evolution equations Lax type. III: the Boussinesq equation, Physics Letters A77 (1980), pp.307-311, in collaboration with M.A. Olshanetsky, A.M. Perelomov and O. Ragnisco.

20 Extension of the Zakharov-Shabat generalized inverse method to solve differential difference and difference difference equations, Il Nuovo Cimento A58 (1980), pp.56-66, in collaboration with O. Ragnisco and M. Bruschi.

21 The non-abelian Toda lattice - discrete analogue of the matrix Schrödinger spectral problem, Journal of Mathematical Physics 21 (1980), pp.2749-2753, in collaboration with M. Bruschi, S.V. Manakov and O. Ragnisco.

22 Bäcklund transformations and nonlinear differential difference equations, Proceedings of the National Academy of Science USA 77 (1980), pp.5025-5027, in collaboration with R. Benguria.

23 Evolution equations associated with the discrete analogue of the matrix Schrödinger spectral problem solvable by the inverse spectral transform, Journal of Mathematical Physics 22 (1981) pp.2463-2471, in collaboration with M. Bruschi and O. Ragnisco.

24 Nonlinear differential difference equations as Bäcklund transformations, Journal of Physics A: Math.Gen. 14 (1981), pp.1083-1098.

25 Bäcklund transformations for nonlinear evolution equations in 2+1dimensions, Physics Letters A81 (1981), pp.419-423, in collaboration with L. Pilloni and P.M. Santini.

26 Integrable three dimensional lattices, Journal of Physics A: Math.Gen. 14 (1981), pp.1567-1575, in collaboration with L. Pilloni and P.M. Santini.

27 The quantum Toda lattice, Physics Letters A88 (1982), pp.7-12, in collaboration with M. Bruschi, M.A. Olshanetsky, A.M. Perelomov and O. Ragnisco.

28 Bäcklund transformations for chiral field equations, Physics Letters A87 (1982), pp.381-384, in collaboration with O. Ragnisco.

29 The chiral field hierarchy, Physics Letters A88 (1982), pp. 379-382, in collaboration with M. Bruschi and O. Ragnisco.

30 The discrete chiral field hierarchy, Lettere al Nuovo Cimento 33 (1982), pp.284-288, in collaboration with M. Bruschi and O. Ragnisco.

31 Nonlinear partial differential equations and Bäcklund related to the 4-dimensional self-dual Yang-Mills equation, Lettere al Nuovo Cimento 33 (1982), pp.263-266, in collaboration with M. Bruschi and O. Ragnisco.

32 Bäcklund transformations vr. Dressing method, Lettere al Nuovo Cimento 33 (1982), pp.401-406, in collaboration with O. Ragnisco and A. Sym.

33 The inverse scattering transform for solving the discrete Sine-Gordon equation, Physics Letters A92 (1982), pp.5-8, in collaboration with L. Pilloni.

34 N-solitons on a vortex filament, Physics Letters A94 (1983), pp.408-411, in collaboration with A. Sym and S. Wojciechowski.

35 Continuous and discrete matrix Burgers hierarchies, Il Nuovo Cimento B74 (1983), pp.33-51, in collaboration with M. Bruschi and O. Ragnisco.

36 A hierarchy of coupled Korteweg-de Vries equations, Physic Letters A95 (1983), pp.7-10.

37 A hierarchy of coupled Korteweg-de Vries equations and the normalization conditions of the Hilbert-Riemann problem, Journal of Physics A: Math.Gen. 16 (1983), pp.2423-2432, in collaboration with A. Sym and S. Wojciechowski.

38 The Bäcklund transformations for nonlinear evolution equations which exhibit exotic solitons, Physics Letters A100 (1984), pp.7-10, in collaboration with O. Ragnisco and A. Sym.

39 Some remarks on the normalization condition problem of the dressing method, Journal of Physics A: Math.Gen. 17 (1984), pp.931-934, in collaboration with O. Ragnisco and A. Sym.

40 Dressing method vs. classical Darboux transformation, Il Nuovo Cimento 83B (1984), pp.34-42, in collaboration with O. Ragnisco and A. Sym.

41 On the generation of internal solitary marine waves, Il Nuovo Cimento 7C (1984), pp.365-77, in collaboration with V. Artale, E. Salusti and F. Zirilli.

42 A new nonlinear Schrödinger equation, its hierarchy and n-soliton solutions, Physics Letters A102 (1984), pp.1-6, in collaboration with G. Neugebauer and R. Meinel.

43 On the Olshanetsky-Perelomov many-body system in an external field, Physics Letters A103 (1984), pp.11-14, in collaboration with S. Wojciechowski.

44 On strong and weak Bäcklund transformations, Journal of Physics A: Math.Gen. 18 (1985), pp.215-9, in collaboration with Z. Popowicz.

45 Approximate inverse spectral transform for the Korteweg-de Vries equation, Journal of Physics A: Math.Gen. 18 (1985), pp.1939-44, in collaboration with O. Ragnisco.

46 Toward an unification of the various techniques used to integrate nonlinear partial differential equations: Bäcklund and Darboux transformations vs. dressing method, Reports in Mathematical Physics 23 (1986), pp.41-56.

47 Sub-algebras of loop algebras and symmetries of the Kadomtsev-Petviashvili equation, Physics Review Letters 55 (1985), pp.2111-3, in collaboration with D. David, N. Kamran and P. Winternitz.

48 Soliton surfaces VII. Relativistic string in external field: general integral and particular solutions, Lettere al Nuovo Cimento 44 (1985), pp.529-36, in collaboration with A. Sym, O. Ragnisco and M. Bruschi.

49 Symmetry reduction for the Kadomtsev-Petviashvili equation using a loop algebra, Journal of Mathematical Physics 27 (1986), pp.1225-37, in collaboration with D. David, N. Kamran and P. Winternitz.

50 Bäcklund transformations and the infinite dimensional Symmetry group of the Kadomtsev-Petviashvili equation, Physics Letters 118A (1986), pp.390-394, in collaboration with D. David and P. Winternitz.

51 Integrable nonlinear equations for water waves in straits of varying depth and width, Studies in Applied Mathematics 76 (1987), pp.133-168, in collaboration with D. David and P. Winternitz.

52 Nonlinear internal waves in a one-dimensional Channel, Il Nuovo Cimento 10C (1987), pp.61-76, in collaboration with V. Artale.

53 Solitons on a relativistic string, preprint DF-INFN N.496 (13/1/86), in collaboration with J. Cieslinski and A. Sym.

54 Equivalent classes of integrable nonlinear evolution equations and generalized Miura transformations, Journal of Physics A: Math.Gen. 20 (1987), pp.313-321, in collaboration with Deng-Yuan Chen and Yi-Shen Li.

55 Hierarchies of integrable equations obtained as non-isospectral (in x and t) deformations of the Schrödinger spectral problem, Physics Letters 119A (1987), pp.453-456.

56 On a new Darboux transformation for the construction of exact solutions of the Schrödinger equation, Inverse Problems 4 (1988), pp.165-172.

57 Non-isospectral deformations and Darboux transformations for the third order spectral problem, Inverse Problems 4 (1988), pp.815-828, in collaboration with O. Ragnisco.

58 The Cylindrical Kadomtsev-Petviashvili Equation; its Kac-Moody-Virasoro Algebra and Relation to the KP equation, Phys. Lett. A129 (1988), pp.165-167, in collaboration with P. Winternitz.

59 Equations Invariant Under the Symmetry Group of the Kadomtsev-Petviashvili Equation, Phys. Lett. A129 (1988), pp.161-164, in collaboration with D. David and P. Winternitz.

60 Alternatives to the Kadomtsev - Petviashvili equation in the description of water waves in more dimensions, Phys. Lett. A135 (1989), pp.453-457.

61 Solitons in Shallow Seas of Variable Depth and in Marine Straits, Stud. Appl. Math. 80 (1989), pp.1-23, in collaboration with D. David and P. Winternitz.

62 Non-classical symmetry reduction: example of the Boussinesq equation, J. Phys. A: Math. Gen. 22 (1989), pp.2915-2924, in collaboration with P. Winternitz.

63 Group theoretical analysis of a rotating shallow liquid in a rigid container, J. Phys. A; Math. Gen. 22 (1989), pp. 4743-4767 in collaboration with M.C. Nucci, C. Rogers and P. Winternitz.

64 Nonlinear surface waves and internal waves in stratified shear flow, Geophysical and Astrophysical Fluid Dynamics 54 (1990), pp 35-48, in collaboration with V. Artale.

65 Analysis of Nonlinear Internal Waves Observed by Landsat Thematic Mapper, Journ. Geoph. Research 95 (1990), pp. 16065-16073, in collaboration with V. Artale, S. Marullo and R. Santoleri.

66 Group invariance of a neo-Hookean system: Incorporation of stretch change, Journal of Elasticity 24 (1990), pp.295-300, in collaboration with C. Rogers.

67 Integrable systems describing surfaces of non-constant curvature, Phys. Lett. A149 (1990), pp. 381-387, in collaboration with A. Sym.

68 A working Algorithm to Isolate Integrable Surfaces in E3, preprint Dip.Fis. INFN N.761del 10/10/1990, in collaboration with A. Sym and Tu Gui-Zhang.

69 Exact solutions of the stimulated Raman Scattering equations, Phys. Rev. A44 (1991), pp. 6057-6070 , in collaboration with C.R. Menyuk and P. Winternitz.

70 Continuous symmetries of discrete equations, Phys. Lett. A152 (1991), pp. 335-338, in collaboration with P. Winternitz.

71 Inhomogeneous Toda Lattice: its hierarchy and Darboux-Bäcklund transformations, Journ. Phys. A: Math.Gen. 24 (1991), pp. 1729-1739, in collaboration with O. Ragnisco.

72 Self-similarity in stimulated Raman scattering, Phys. Rev. Lett. 69 (1992), pp. 3048-3051, in collaboration with, C.R. Menyuk and P. Winternitz.

73 Symmetry Group of partial differential equations and of differential difference equations: the Toda lattice vs the Korteweg de Vries equation, J. Phys. A: Math Gen. 25 (1992), pp. L975-L979, in collaboration with M.A. Rodriguez.

74 On non-isospectral flows, Painlevè equations and symmetries of differential difference equations, Teor. Math. Phys. 93 (1992), pp. 473-480, in collaboration with M.A. Rodriguez and O. Ragnisco.

75 Quasi-Solitons on a diatomic chain at room temperature, Phys. Rev. B48 (1993), pp.10168-10182, in collaboration with A. Campa, A. Giansanti, O. Ragnisco and A. Tenenbaum,.

76 Symmetries and Conditional symmetries of Differential-Difference Equations, J. Math Phys 34 (1993), pp. 3713-3730, in collaboration with P. Winternitz.

77 Construction of higher local 2+1dimensional exponential lattice equations, Canadian Journal of Physics 72 (1994), pp. 439-441, in collaboration with O. Ragnisco and A.B. Shabat.

78 Similarity reduction and perturbation solution of the stimulated Raman scattering equations in the presence of dissipation, Phys. Rev. A49 (1994), pp.2844-2852, in collaboration with C.R. Menyuk and P. Winternitz.

79 Simmetries and conditional symmetries of a non-relativistic Chern-Simons system, Annals of Physics 230 (1994), pp.101-117, in collaboration with L. Vinet and P. Winternitz.

80 Irrotational water waves and the complex Korteweg-de Vries equation, Physica D98 (1996), pp.510-514 in collaboration with M. Sanielevici.

81 Symmetries of discrete dynamical systems, J. Math. Phys. 37 (1996), pp.5551-5576, in collaboration with P. Winternitz.

82 Lie group formalism for differrence equations, J. Phys. A: Math. Gen. 30 (1997), pp.633-649, in collaboration with L. Vinet and P. Winternitz.

83 Conditions for the existence of higher symmetries of evolutionary equations on the lattice, J. Math. Phys. 38 (1997), pp.6648-6674, in collaboration with R. Yamilov.

84 Symmetries of the Discrete Burgers Equations, J. Phys. A: Math. Gen. A32 (1999), pp.2685-2695, in collaboration with R. Hernandez Heredero and P. Winternitz.

85 Free Electron Lasers and soliton propagation, Phys. Letters A256 (1999), pp.253-256, in collaboration with G. Dattoli and M. Mattioli.

86 On higher order Riccati equations as Bäcklund transformations, J. Phys. A.: Math. Gen. 32 (1999), pp. 3931-3937, in collaboration with M. Grundland.

87 Dilation symmetries and equations on the lattice, J. Phys. A: Math. Gen. 32 (1999), pp. 8317-8323, in collaboration with R. Yamilov.

88 Lie symmetries for integrable evolution equations on the lattice, J. Phys. A: Math. Gen. 32 (1999), pp. 8303-8316, in collaboration with M.A. Rodriguez.

89 Non-point Integrable Symmetries for Equations on the Lattice, J. Phys. A: Math. Gen 33 ( 2000), pp. 4809-4823, in collaboration with R. Yamilov.

90 Exponential operators and generalized difference equations, Nuovo Cimento 115B (2000), pp. 653-662, in collaboration with G. Dattoli.

91 Lie algebra contractions and symmetries of the Toda hierarchy, J. Phys. A: Math. Gen. 33 (2000), pp. 5025-5040 in collaboration with R. Hernandez Heredero, M.A. Rodriguez and P. Winternitz.

92 Lie point symmetries of difference equations and the lattice, J. Phys. A: Math. Gen. 33 (2000), pp. 8507-8523, in collaboration with S. Tremblay and P. Winternitz.

93 Discrete derivatives and symmetries of difference equations, J. Phys. A: Math. Gen. 34 (2001), pp. 2023-2030, in collaboration with J. Negro and M.A. del Olmo.

94 Discrete third-order spectral problems and a new Toda-type equation, J. Phys. A: Math. Gen. 35 (2002), pp. L67-L73, in collaboration with A.M. Grundland.

95 Relation between Bäcklund transformations and higher continuous symmetries of the Toda equation, J. Phys. A: Math. Gen. 34 (2001), pp. 2459-2465, in collaboration with R. Hernandez Heredero, M.A. Rodriguez e P. Winternitz.

96 Integrable hierarchies of nonlinear difference-difference equations and symmetries, J. Phys. A: Math. Gen. 34 (2001), pp. 10357-10368, in collaboration with L. Martina.

97 On the integrability of a new discrete nonlinear Schrödinger equation, J. Phys. A: Math. Gen. 34 (2001), pp. L553-L562, in collaboration with R. Yamilov.

98 Lie symmetries of multi-dimensional difference equations, J. Phys. A: Math. Gen. 34 (2001), pp. 9507-9524, in collaboration with S. Tremblay and P. Winternitz.

99 Lie point symmetries and commuting flows for equations on lattices, J. Phys. A: Math. Gen. 35 (2002), pp. 2249-2262, in collaboration with P. Winternitz.

100 Transversal perturbation of longitudinal soliton modes on a Free Electron Laser, Phys. Lett. A307 (2003), pp. 239-243, in collaboration with G. Dattoli and M. Mattioli.

101 Discrete CP1 sigma models and surfaces in R3, J. Phys. A: Math. Gen. 36 (2003), pp. 4599-4616, in collaboration with A.M. Grundland and L.Martina.

102 The SPARC project: a high-brightness electron beam source at LNF to drive a SASE-FEL experiment, Nucl. Instrum. Methods Phys. Res. A; Accel. Spectrom. Detect. Assoc. Equip.507 (2003), pp. 345-349, in collaboration with D. Alesini, S. Bertolucci, M.E. Biagini, C. Biscari, R. Boni, M. Boscolo, M. Castellano, A. Clozza, G. Di Pirro, A. Drago, A. Esposito, M. Ferrario, V. Fusco, A. Gallo, A. Ghigo, S. Guiducci, M. Incurvati, P. Laurelli, C. Ligi, F. Marcellini, M. Migliorati, C. Milardi, L. Palumbo, L. Pellegrino, M. Preger, P. Raimondi, R. Ricci, C. Sanelli, F. Sgamma, B. Spataro, M. Serio, A. Stecchi, A. Stella, F. Tazzioli, C. Vaccarezza, M. Vescovi, C. Vicario, M. Zobov, E. Acerbi, F. Alessandria, D. Barni, G. Bellomo, I. Boscolo, F. Broggi, S. Cialdi, C. DeMartinis, D. Giove, C. Maroli, V. Petrillo, M. Rome’, L. Serafini, E. Chiadroni, G. Felici, M. Mastrucci, M. Mattioli, G. Medici, G.S. Petrarca, L. Catani, A. Cianchi, A. D’Angelo, R. Di Salvo, A. Fantini, D. Moricciani, C. Schaerf, R. Bartolini, F. Ciocci, G. Dattoli, A. Doria, F. Flora, G.P. Gallerano, L. Giannessi, E. Giovenale, G. Messina, L. Mezi, P.L. Ottaviani, L. Picardi, M. Quattromini, A. Renieri, C. Ronsivalle, L. Avaldi, C. Carbone, A. Cricenti, A. Pifferi, P. Perfetti, T. Prosperi, Albertini, V. Rossi, C. Quaresima, N. Zema.

103 Conceptual design of a high-brightness linac for soft X-ray SASE-FEL source, Nucl. Instrum. Methods Phys. Res. A; Accel. Spectrom. Detect. Assoc. Equip. 507 (2003), pp. 502-506, in collaboration with D. Alesini, S. Bertolucci, M.E. Biagini, C. Biscari, R. Boni, M. Boscolo, M. Castellano, A. Clozza, G. Di Pirro, A. Drago, A. Esposito, M. Ferrario, V. Fusco, A. Gallo, A. Ghigo, S. Guiducci, M. Incurvati, P. Laurelli, C. Ligi, F. Marcellini, M. Migliorati, C. Milardi, L. Palumbo, L. Pellegrino, M. Preger, P. Raimondi, R. Ricci, C. Sanelli, F. Sgamma, B. Spataro, M. Serio, A. Stecchi, A. Stella, F. Tazzioli, C. Vaccarezza, M. Vescovi, C. Vicario, M. Zobov, E. Acerbi, F. Alessandria, D. Barni, G. Bellomo, I. Boscolo, F. Broggi, S. Cialdi, C. DeMartinis, D. Giove, C. Maroli, V. Petrillo, M. Rome’, L. Serafini, E. Chiadroni, G. Felici, M. Mastrucci, M. Mattioli, G. Medici, G.S. Petrarca, L. Catani, A. Cianchi, A. D’Angelo, R. Di Salvo, A. Fantini, D. Moricciani, C. Schaerf, R. Bartolini, F. Ciocci, G. Dattoli, A. Doria, F. Flora, G.P. Gallerano, L. Giannessi, E. Giovenale, G. Messina, L. Mezi, P.L. Ottaviani, L. Picardi, M. Quattromini, A. Renieri, C. Ronsivalle, L. Avaldi, C. Carbone, A. Cricenti, A. Pifferi, P. Perfetti, T. Prosperi, Albertini, V. Rossi, C. Quaresima, N. Zema.

104 Lie discrete symmetries of lattice equations, J. Phys. A: Math. Gen. 37 (2004), pp. 1711-1725, in collaboration with M.A. Rodriguez.

105 Integrability Conditions for n and t Dependent Dynamical Lattice Equations, Jour. Nonlin. Math. Phys. 11 (2004), pp. 75-101, in collaboration with R. Yamilov.

106 The Discrete Nonlinear Schrödinger Equation and its Lie symmetry reductions, Jour. Nonlin. Math. Phys. 10 Suppl. 2 (2003), pp. 77-94, in collaboration with R. Hernandez Heredero.

107 Lorentz and Galilei Invariance on Lattices, Phys. Rev. D. 69 (2004) 105011, in collaboration with P. Tempesta and P. Winternitz.

108 Discrete $q$--derivatives and symmetries of $q$--difference equations, J. Phys. A. 37 (2004), pp. 3459-3473, in collaboration with J. Negro and M. dell’Olmo

109 Umbral Calculus, Difference Equations and the Discrete Schroedinger Equation, J. Math. Phys. 45 (2004), pp. 4077- 4105, in collaboration with P. Tempesta and P. Winternitz.

110 Multiscale Analysis of Discrete Nonlinear Evolution Equations: The Reduction of the dNLS, J. Nonl. Math. Phys. 12 Suppl. 1 (2005) 440-448, in collaboration with R. Hernandez Heredero.

111 Multiple-scale analysis of discrete nonlinear partial difference equations: the reduction of the lattice potential KdV, J. Phys. A: Math. Gen. 38 (2005) 7677-7689.

112 Asymptotic symmetries of difference equations on a lattice, Journal of Nonlinear Mathematical Physics, Volume 12 Supplement 2, 2005 pp. 137-146 in collaboration with G Gaeta and R Mancinelli, .

113 Continuous symmetries of difference equations, J. Phys. A: Math. Gen. 39 No 2 (13 January 2006) R1-R63, in collaboration with P. Winternitz.

114 Discrete reductive perturbation technique , J. Math. Phys. 47, 043509 (2006) in collaboration with M. Petrera.

115 On a discrete Davey-Stewartson system Inverse Problems, 22 1677-1688 (2006) in collaboration with Gegenhasi and X B Hu.

116 CONTINUOUS SYMMETRIES OF THE LATTICE POTENTIAL KDV EQUATION, 2007, J. Phys. A. 40, 4141-4159, in collaboration with M. Petrera.

117 THE LATTICE SCHWARZIAN KDV AND ITS SYMMETRIES, Journal of Physics A: Mathematical and Theoretical, 40, pp. 12753-12761 2007 ISSN: 1751-8113, in collaboration with Matteo Petrera and Christian Scimiterna.

118 A difference-analogue of Davey-Stewartson system: discrete Gram-type determinant solution and Lax pair, 2007 Journal of Physics A: Mathematical and Theoretical, 40, pp. 12741-12751, ISSN: 1751-8113, in collaboration with Gegenhasi, Xing Biao Hu and Satoshi Tsujimoto. .

119 Multiscale expansion of the lattice potential KdV equation on function of infinite order of slow-varyness, 2007 Journal of Physics A: Mathematical and Theoretical, 40, pp. F831-F840 ISSN: 1751-8113 in collaboration with R. Hernandez Heredero, M. Petrera and C. Scimiterna, .

120 Asymptotic symmetries and integrability: the KdV case, EuroPhysics Letters (2007), vol. 80, pp. 60005 ISSN: 0295-5075 in collaboration with M.A. RODRIGUEZ.

121 Heisenberg Algebra, Umbral Calculus and Orthogonal Polynomials, J. Math. Phys. 49, 053509 (2008) arXiv:0712.2957, in collaboration with G. Dattoli and P. Winternitz,

122 Multiscale expansion on the lattice and integrability of partial difference equations - , J. Phys. A: Math. Theor. 41 No 31 (8 August 2008) 315208 (12pp), arXiv:0710.5299, in collaboration with Rafael Hernandez Heredero, Matteo Petrera and Christian Scimiterna,

123 On Miura transformations and Volterra-type equations associated with the Adler-Bobenko-Suris equations, SIGMA 4 (2008), Paper 077, 14 pp in collaboration with M. Petrera, C. Scimiterna and R. Yamilov,

124 Multiscale expansion and integrability properties of the lattice potential KdV equation, J. Nonlinear Math. Phys. 15 (2008), suppl. 3, 323-333 in collaboration with R. Heredero, M. Petrera and C. Scimiterna,

125 On the integrability of the discrete nonlinear Schroedinger equation, Europhys. Lett. 84 (2008), 10003 in collaboration with M. Petrera and C. Scimiterna,

126 The generalized symmetry method for discrete equations. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, (2009) vol. 42; p. 454012, ISSN: 1751-8113, doi: 10.1088/1751-8113/42/45/454012 in collaboration with R.I. YAMILOV.

127 The Kundu–Eckhaus equation and its discretizations. Journal of Physics A: Mathematical and Theoretical, 42; p. 465203, (2009) doi: 10.1088/1751-8121/42/45/450301, in collaboration with C. SCIMITERNA.

128 Multiscale reduction of discrete nonlinear Schrödinger equations Journal of Physics A: Mathematical and Theoretical, 42; p. 454011, (2009) doi: 10.1088/1751-8113/42/45/45401 in collaboration with M. PETRERA and C. SCIMITERNA.

129 A discrete linearizability test based on multiscale analysis, (2010) Journal of Physics A: Mathematical and Theoretical, 43 (50), art. no. 502002 in collaboration with R.H. Heredero and C. Scimiterna.

130 Multiple-scale analysis of dynamical systems on the lattice, (2010) Journal of Mathematical Analysis and Applications, Volume 376, Issue 1, 1 April 2011, Pages 247-258 in collaboration with P. Tempesta.

131 lambda-symmetries for discrete equations, (2010) Journal of Physics A: Mathematical and Theoretical, 43 (29), art. no. 292001 in collaboration with M.A. Rodríguez.

132 Lie point symmetries of differential-difference equations, (2010) Journal of Physics A: Mathematical and Theoretical, 43 (29), art. no. 292002 in collaboration with P. Winternitz and R.I. Yamilov.

133 Integrability test of discrete nonlinear Schrödinger equations via multiscale reduction, (2010) Applicable Analysis, 89 (4), pp. 507-527 in collaboration with C. Scimiterna.

134 DISCRETE MULTISCALE ANALYSIS: A BIATOMIC LATTICE SYSTEM, JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 17 (3): 357-377 (2010) DOI: 10.1142/S1402925110000957 in collaboration with G. A. Cassatella Contra.

135 C-Integrability Test for Discrete Equations via Multiple Scale Expansions, SIGMA, 6: Art. No. 070 (2010) DOI: 10.3842/SIGMA.2010.070 in collaboration with C. Scimiterna.

136 Linearizability of Nonlinear Equations on a Quad-Graph by a Point, Two Points and Generalized Hopf-Cole TransformationsSIGMA 7 (2011), 079, 24 pages arXiv:1108.3648, in collaboration with C. Scimiterna.

137 Symmetries of the Continuous and Discrete Krichever-Novikov Equation SIGMA 7 (2011), 097, 16 page, in collaboration with P. Winternitz and R. I. Yamilov.

138 Are there contact transformations for discrete equations? 2011 J. Phys. A: Math. Theor. 44 265201 doi 10.1088/1751-8113/44/26/265201 in collaboration with Z. Thomova and P. Winternitz.

139 Generalized symmetry integrability test for discrete equations on the square lattice 2011 J. Phys. A: Math. Theor. 44 145207 doi:10.1088/1751-8113/44/14/145207 in collaboration with R.I. Yamilov.

140 Integrability of differential-difference equations with discrete kinks, Theor. Math. Phys.,2011, Volume 167, Number 3, Pages 826-842, in collaboration with C> Scimiterna.

141 Contact transformations for difference schemes, 2012 J. Phys. A: Math. Theor. 45 022001 doi: 10.1088/1751-8113/45/2/022001 in collaboration with C. Scimiterna, Z. Thomova and P. Winternitz.

142 On Fourier integral transforms for q-Fibonacci and q-Lucas polynomials, 2012 J. Phys. A: Math. Theor. 45 195206 doi:10.1088/1751-8113/45/19/195206 in collaboration with N. Atakishiyev, P. Franco and O. Ragnisco.

143 Classification of discrete systems on a square lattice, Theor. Math. Phys. (2012), 172, 1097-1108, in collaboration with RH Heredero and C Scimiterna.

144 CLASSIFICATION OF MULTILINEAR REAL QUADRATIC PARTIAL DIFFERENCE EQUATIONS LINEARIZABLE BY POINT AND HOPF–COLE TRANSFORMATIONS, Inter. J. Geo. Meth. Mod. Phys. 9 (2012) 1260004 (8 pages), World Scientific Publishing Company DOI: 10.1142/S0219887812600043 in collaboration with C Scimiterna.

145 λ-Symmetries for the Reduction of Continuous and Discrete Equations,Acta Applicandae Mathematicae, 2012, Volume 122, Issue 1, pp 311-321 in collaboration with MC Nucci and MA Rodríguez.

146 λ-symmetries and Jacobi last multiplier, Nonlinear Analysis: Real World Applications, Volume 14, Issue 2, April 2013, Pages 1092–1101, in collaboration with MC Nucci.

147 The Jacobi last multiplier for difference equations, J. Phys. A: Math. Theor. 45 (2012) 275205 doi:10.1088/1751-8113/45/27/275205, arXiv:1202.6208, in collaboration with MA Rodriguez.

148 Lie groups and numerical solutions of differential equations: Invariant discretization versus differential approximation in collaboration with P Winternitz - Acta Polytech. Prace CVUT, in press, arXiv preprint arXiv:1304.7016, 2013

149 Three-point partial difference equations linearizable by local and nonlocal transformations, J. Phys. A: Math. Theor. 46, (2013) 25205-25217(13) in collaboration with C Scimiterna.

150 Classification of discrete equations linearizable by point transformation on a square lattice - Front. Math. in China, in press 2013, in collaboration with C Scimiterna

151 On the construction of partial difference schemes I: the Clairaut, Schwarz, Young theorem on the lattice, J. Phys. A: Math. Theor. , in press, in collaboration with M.A. Rodriguez

152 Linearization through symmetries for discrete equations, J. Phys. A: Math. Theor. , in press, in collaboration with C. Scimiterna.

153 Four Points Linearizable Lattice Schemes, J. Geom. Symmetry Phys. in press, arXiv:1301.0732 in collaboration with C Scimiterna.











Publications in Conference Proceedings



1 Perturbative approach to some one-dimensional many-body problems, in Proceedings of the 1977 European Symposium on Few Particle Problems in Nuclear Physics, edited by B.Kuhn e K.Moller , Zentralinstitut fur Kernforschung Rossendorf (Dresden, 1977) pp.17-18, in collaboration with O. Ragnisco.

2 Alcune tendenze attuali nell'interpretazione della meccanica quantistica: confronto con le prospettive ideologiche emetodologiche degli anni '20, in Matematica eFisica: Struttura e Ideologia, edited by E. Donini, A. Rossi e T. Tonietti, De Donato (Bari, 1977).

3 The spectral transform as a tool for solving nonlinear discrete evolution equations, in Proceedings of the IX International Seminar on Nonlinear Problems in Theoretical Physics, edited by A.F. Ranada, Lecture Notes in Physics vol.98, Springer Verlag (Heidelberg, 1979).

4 Second Workshop on nonlinear evolution equations and systems - the Ortodox Academy, Kolimbary near, Crete; august 13-28/1983 - a short summary, Physica D11 (1984), pp.389-391, pp. 399-416, in collaboration with F. Calogero and A. Verganelakis.

5 Integrable nonlinear partial differential equations in the description of water flow in channels or straits of variable width and depth, in Systems Dynamiques nonlineaires, integrabilite' et comportement qualitatif, P. Winternitz ed., Seminaire de Mathematique Superioures Vol. 102, Les Presse de l'Universite' de Montreal, Montreal (1986).

6 Sistemi integrabili nella descrizione di onde in stretti o canali di profondita' o larghezza variabili, publicato nel Bollettino Geofisico del G.N.F.A.O. e I.F.A.,Aspetti della Fluidodinamica Geofisica Italiana R. Purini and M. Severini eds., Roma (1987), pp.229-240.

7 Darboux and Bäcklund Transformations for the Schrödinger equation, in Inverse Problems: an interdisciplinary study, P.C. Sabatier ed., Academic Press, New York (1987).

8 Hierarchies of Nonlinear Integrable Evolution Equations with Variable Coefficients. The variable coefficient KdV and Boussinesq equations, in the Proceedings IV Workshop on Nonlinear Evolution Equations and Dyamical Systems edited by J.J. Leon (World Scientific, Singapore, 1988) .

9 Solitary Waves in Straits, nei Proceedings IV Workshop on Nonlinear Evolution Equations and Dyamical Systems edited by J.J. Leon (World Scientific, Singapore, 1988), in collaboration with V. Artale.

10 Integrable systems and water waves. An example of symmetry analysis applied to a physical problem, in Symmetries and Nonlinear Phenomena, edited by D. Levi and P. Winternitz (World Scientific, Singapore, 1988).

11 Introduction, in Symmetries and Nonlinear Phenomena, edited by D. Levi and P. Winternitz (World Scientific, Singapore, 1988), in collaboration with P. Winternitz.

12 Nonlinear internal solitary waves in straits with varying width and depth, in Nonlinear Topics in Ocean Physics edited by A.R. Osborne (Elsevier Publishing Co., Amsterdam, 1989).

13 Preface, Nonlinear Evolution Equations and Dynamical Systems, edited by S. Carillo e O. Ragnisco, Springer Verlag, Berlin 1990, in collaboration with F. Calogero and A. Verganelakis.

14 Vibrational properties and energy transport in Acetanilide by molecular dynamics, in Davydov’s Soliton Revisited. Self-Trapping of Vibrational Energy in Protein, edited by P.L. Chrisiansen and A.C. Scott, Plenum Press, N.Y. 1990, in collaboration with A. Campa, A. Giansanti, O. Ragnisco and A. Tenenbaum.

15 Integrable nonlinear evolution equations in the description of waves in the shallow-water long-wave approximation, in Mathematical Theory of Solitons edited by P. Olver and D. Sattinger (Springer Verlag, I.M.A. Series Vol.20, New York, 1990).

16 Kadomtsev-Petviashvili equations in the description of water waves, in Proceedings della International Conference on Nonlinear Physics Shanghai (Cina R.P.) 24-30/4/1989, eds. Chao-Hao Gu, Yi-Sheng Li e Gui-Zhang Tu (Springer Verlag New York 1990).

17 Solitons in stratified shear flow, in Nonlinear Phenomena in Physics of Fluids and Plasmas, edited by G. Maino, L. Franzoni and M. Pettini, World Scientific, Singapore 1991, in collaboration with V. Artale, pp. 67-80.

18 Introduction, Painleve' Transcendents, their asymptotics and Physical applications, D. Levi and P. Winternitz eds., Nato Asi Series B. N. 278, Plenum Press, New York (1992) pp. VII-XI.

19 Symmetry reduction for the stimulated Raman scattering equations and the asymptotic of Painlevè V via Boutroux Transformation, D. Levi, in Painleve' Transcendents, their asymptotics and Physical applications, D. Levi and P. Winternitz eds., Nato Asi Series B. N. 278, Plenum Press, New York (1992), pp. 353-60.

20 Lattice equations with N-dependent coefficients associated to the discrete Schroedinger spectral problem, in Nonlinear Evolution Equations and Dynamical Systems, edited by M. Boiti, L. Martina and F. Pempinelli, World Scientific, Singapore 1992, pp. 225-232.

21 Inhomogeneous Toda lattices and their symmetries, in Group Theory in Physics, edited by A. Frank, T.H. Seligman and K.B. Wolf, AIP, New York, 1992, pp. 97-108.

22 Symmetries of a classical Chern-Simons theory, in Quantum Groups, Integrable Models and Statistical Systems, edited by J. LeTourneaux and L. Vinet, World Scientific, Singapore 1993, in collaboration with L. Vinet and P. Winternitz, pp. 148-158.

23 Symmetries of differential equations on a lattice. An example: the Toda lattice, in Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, edited by N.H. Ibragimov, M. Torrisi and A. Valenti, Kluwer Academic Publisher, Dordrecht, 1993, in collaboration with P. Winternitz, pp. 265-272.

24 Dimensional reduction for equations involving discrete and continuous variables, in Applications of Analytic and geometric Methods to Nonlinear Differential Equations, edited by P.A. Clarkson, Kluwer Academic Publishers, Dordrecht 1993, in collaboration with P. Winternitz, pp. 405-413.

25 Preface, in Self-Similarity in Stimulated Raman Scattering, edited by D. Levi, C.R. Menyuk and P. Winternitz, Les Publications CRM 1994, in collaboration with C.R. Menyuk and P. Winternitz.

26 Self-similarity in stimulated Raman scattering, in Self-Similarity in Stimulated Raman Scattering, edited by D. Levi, C.R. Menyuk and P. Winternitz, Les Publications CRM 1994, in collaboration with P. Winternitz, pp. 29-54.

27 Continuous symmetries of differential difference equations, in Modern Group Theoretical Methods in Physics, edited by J. Bertrand, M. Flato, J.-P. Gazeau, M. Irac-Astaud and D. Sternheimer, Kluwer Academic Publisher, Dordrecht 1995, in collaboration with P. Winternitz, pp. 271-282.

28 Simmetry analysis of discrete physical systems, con P. Winternitz, Nonlinear Physics, Theory and experiment, editori E. Alfinito, M. Boiti, L. Martina and F. Pempinelli, World Scientific Singapore 1996, pp. 199-216.

29 Lie point symmetries of differential difference equations, Symmetries and Integrability of Difference Equations, editors D. Levi, L. Vinet and P. Winternitz, American Mathematical Society Providence 1996, pp. 199-208, in collaboration with P. Winternitz.

30 Preface, Symmetries and Integrability of Difference Equations, eds. D. Levi, L. Vinet and P. Winternitz, American Mathematical Society Providence 1996, in collaboration with L. Vinet and P. Winternitz.

31 Symmetries of discrete physical systems, in Proceedings of the IV Wigner Symposium, edited by N.M. Atakishiyev, T.H. Seligman and K.B. Wolf, World Scientific Singapore 1996, in collaboration with L. Vinet and P. Winternitz, pp.382-391.

32 Equations defined on the lattice and their solutions, in Nonlinearity and Geometry, edited by D. Wojcik and J. Cieslinski, Polish Scientific Publisher PWN, Varsavia 1998, pp. 179-206.

33 Symmetries and generalized symmetries for discrete dynamical systems, in Symmetries and Integrability of Difference Equations, edited by P.A. Clarkson and F.W. Nijhoff, Cambridge University Press, Cambridge 1998, pp. 261-274.

34 Discrete Painleve Equations from Nonisospectral Soliton Equations, in Symmetries and integrability of difference equations, edited by D. Levi and O. Ragnisco, AMS/CRM 2000, in collaboration with R. Quispel.

35 Symmetry Preserving Discretization of the Burgers Equation, , in Symmetries and integrability of difference equations, edited by D. Levi and O. Ragnisco, AMS/CRM 2000, in collaboration with R. Hernandez Heredero and P. Winternitz.

36 Dressing Method and Backlund and Darboux Transformations, in Bäcklund & Darboux Transformations:The Geometry of Soliton Theory , edited by A. Coley, D. Levi, R. Milson, C. Rogers and P. Winternitz, AMS/CRM 2001, in collaboration with O. Ragnisco,.

37 Symmetries of Differential Difference equations and Lie Algebra Contractions, in Bäcklund & Darboux Transformations:The Geometry of Soliton Theory, edited by A. Coley, D. Levi, R. Milson, C. Rogers and P. Winternitz, AMS/CRM 2001, in collaboration with R. Hernandez Heredero, M A Rodriguez and P. Winternitz.

38 Symmetries of the discrete nonlinear Schroedinger equation, in collaboration with R. Hernandez Heredero and P. Winternitz, in 14th International Workshop “Nonlinear Evolution Equations and Dynamical Systems”, 29 June – 7 July 2000, Gokova, Turkey, Math. Theor. Phys. 127 (2001), pp. 729-737

39 Lie symmetries of difference equations, in DI-CRM Workshop, Prague, 18-21/6/2000, in collaboration with J.Negro and M.A.del Olmo, Czechoslovak Journal of Physics 51(2001), pp. 341-348.

40 Continuous symmetries of equations on lattices, in DI-CRM Workshop, Prague, 18-21/6/2000, in collaboration with S.Tremblay and P.Winternitz, Czechoslovak Journal of Physics 51(2001), pp. 349-356.

41 Lie Symmetries for Lattice Equations, in GROUP 24: Physical and Mathematical Aspects of Symmetries: Proceedings of the 24th International Colloquium on Group Theoretical Methods in Physics, Paris, 15-20 July 2002, Ed. J-P Gazeau, R Kerner, J-P Antoine, S Métens, J-Y Thibon, IOP Publishing 2003, pp. 103—111.

42 Conceptual Design of a Soft X-ray SASE-FEL Source, in X-Ray and Inner-Shell Processes. 19th International Conference, AIP Conference Proceedings -- January 24, 2003 -- Volume 652, Issue 1, pp. 53-58 in collaboration with D. Alesini, S. Bertolucci, M.E. Biagini, C. Biscari, R. Boni, M. Boscolo, M. Castellano, A. Clozza, G. Di Pirro, A. Drago, A. Esposito, M. Ferrario, V. Fusco, A. Gallo, A. Ghigo, S. Guiducci, M. Incurvati, P. Laurelli, C. Ligi, F. Marcellini, M. Migliorati, C. Milardi, L. Palumbo, L. Pellegrino, M. Preger, P. Raimondi, R. Ricci, C. Sanelli, F. Sgamma, B. Spataro, M. Serio, A. Stecchi, A. Stella, F. Tazzioli, C. Vaccarezza, M. Vescovi, C. Vicario, M. Zobov, E. Acerbi, F. Alessandria, D. Barni, G. Bellomo, I. Boscolo, F. Broggi, S. Cialdi, C. DeMartinis, D. Giove, C. Maroli, V. Petrillo, M. Rome’, L. Serafini, E. Chiadroni, G. Felici, M. Mastrucci, M. Mattioli, G. Medici, G.S. Petrarca, L. Catani, A. Cianchi, A. D’Angelo, R. Di Salvo, A. Fantini, D. Moricciani, C. Schaerf, R. Bartolini, F. Ciocci, G. Dattoli, A. Doria, F. Flora, G.P. Gallerano, L. Giannessi, E. Giovenale, G. Messina, L. Mezi, P.L. Ottaviani, L. Picardi, M. Quattromini, A. Renieri, C. Ronsivalle, L. Avaldi, C. Carbone, A. Cricenti, A. Pifferi, P. Perfetti, T. Prosperi, Albertini, V. Rossi, C. Quaresima, N. Zema.

43 Lie Symmetries for Lattice Equations, in Difference and Differential Equations – eds S. Elaydi, G. Ladas, J-H. Wu, and X-F. Zou, AMS, 2004, pp. 201-214.

44 Multi-scale reduction for differential difference equations and integrability, in NONLINEAR EVOLUTION EQUATIONS AND DYNAMICAL SYSTEMS Proceedings of the ICM2002 Satellite Conference Yellow Mountains, China 15 - 18 August 2002, edited by Cheng Y., Hu S., Li Y-S., Peng C-K, Wolrd Scientific Singapore 2003, pp. 79-89.

45 Discrete Lie symmetries for difference equations, in Group Theory and Numerical Analysis - P. Winternitz, D. Gomez-Ullate, A. Iserles, D. Levi, P. J. Olver, R. Quispel, and P. Tempesta, Editors - AMS, 2005, 298 pp., Softcover, ISBN 0-8218-3565-3, CRMP/39, con M. A. Rodríguez, pp. 179—189.

46 D. Levi, J. Negro and M. del Olmo, Discrete equations and Umbral calculus, in Proceedings of XXV International Colloquium on Group Theoretical Methods in Physics, IOP Conference Series 185, Eds. G.S. Pogosyan, L.E. Vicent, and K.B. Wolf, (IOP/Canopus, Bristol, 2005), pp.223-228.

47 JI X-D, LEVI D., PETRERA M. (2007). Multiscale expansion of the lattice Sine-Gordon equation. In: Proceedings of the International Conference Difference Equations, Special Functions and Orthogonal Polynomials. International Conference Difference Equations, Special Functions and Orthogonal Polynomials. Munchen. 25-30 July 2005. (pp. 305-314). SINGAPORE: World Scientific (SINGAPORE). Eds. S. Elaydi, J. Cushing, R. Lasser, V. Papageorgiou, A. Ruffing and V. Van Assche.

48 D. Levi, "Lie symmetries of differential and difference equations", in Integrable Systems - Theory and Applications, Proceedings of CCAST (World Laboratory) Workshop held in Beijing, P.R. China Dec. 22-28, 2008, eds. X-B Hu and Q-P Liu, Beijing 2008, pp. 1-81.

49 LEVI D., OLVER P, THOMOVA Z, WINTERNITZ P (2009). Symmetries and integrability of difference equations. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, vol. 42; p. 450301, ISSN: 1751-8113, doi: 10.1088/1751-8121/42/45/450301

50 D. Levi and C. Scimiterna, Integrability of the Kruskal—Zabusky Discrete Equation by Multiscale Expansion, AIP Conf. Proc. Volume 1212, Proceedings of the First International Workshop Beijing (China), 15–21 July 2009 Editor(s): Wen Xiu Ma,  Xing-biao Hu,  Qingping Liu, doi:10.1063/1.3367081 pp. 66-80.

51 D. Levi and R. I. Yamilov, Integrability Test for Discrete Equations, AIP Conf. Proc. Volume 1323, Symmetries in Nature: Symposium in Memoriam Marcos Moshinsky, Cuernavaca, Mexico, 7-14 August 2010 Editors: Kurt B. Wolf, Luis Benet, Juan Mauricio Torres, Peter O Hess, ISBN 978-0-7354-0877-7,pp. 203-214









Books and contributions to Books



1 Esercizi di Fisica per Biologia e Scienze Naturali, CISU Roma, 1984), in collaboration with C.Coluzza e V.Ferrari.

2 Symmetries and Nonlinear Phenomena, edited by D. Levi and P. Winternitz (World Scientific, Singapore, 1988).

3 Higher order Kadomtsev-Petviashvili equation in the description of water waves, in Sbornik Asymptotic methods in Mathematical Physics, annual publication in Russian of the Mathematical Institute of the Russian Academy of Sciences, Ufa, 1990 pp.126-156.

4 Painleve' Transcendents, their asymptotics and Physical applications, D. Levi and P. Winternitz eds., Nato Asi Series B. N. 278, Plenum Press, New York (1992).

5 Self-Similarity in Stimulated Raman Scattering, edited by D. Levi, C.R. Menyuk and P. Winternitz, Les Publications CRM 1994.

6 Symmetries and Integrability of Difference Equations, edited by. D. Levi, L. Vinet and P. Winternitz, American Mathematical Society Providence 1996

7 Symmetries and integrability of difference equations, SIDE III, edited by D. Levi and O. Ragnisco, AMS/CRM 2000.

8 Bäcklund & Darboux Transformations:The Geometry of Soliton Theory, edited by A. Coley, D. Levi, R. Milson, C. Rogers and P. Winternitz, AMS/CRM 2001.

9 Symmetries and Integrability of Difference Equations, with P.Winternitz and R.Yamilov, in preparation.

10 Group Theory and Numerical Analysis - P. Winternitz, D. Gomez-Ullate, A. Iserles, D. Levi, P. J. Olver, R. Quispel, and P. Tempesta, Editors - AMS, 2005, 298 pp., Softcover, ISBN 0-8218-3565-3, CRMP/39.

11 Delay-differential equations, in Encyclopedia of Nonlinear Science Edited by: Alwyn Scott Hardback Book, 2004, ISBN 1579583857, pp. 189-191.

12 Backlund transformations, in Encyclopedia of Mathematical Physics, editors Jean-Pierre Françoise, Greg Naber, Tsou Sheung Tsun, Elsevier 2006.

13 LEVI D. (2009). IL CIBER NELL'ESPERIENZA DEL SUO PRIMO COORDINATORE. In: GARGIULO P.BOGLIOLO D.. CIBER 1999-2009. MILANO: LediPublishing, ISBN/ISSN: 978-88-95994-09-3

14 Symmetries and Integrability of Difference Equations, Edited by: Decio Levi, Peter Olver, Zora Thomova and Pavel Winternitz, Series: London Mathematical Society Lecture Note Series(No. 381), ISBN:9780521136587 (2011) 360pages


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