Analytic doubly periodic wave patterns for the integrable discrete nonlinear Schrödinger (Ablowitz-Ladik) model

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 349, Issue 6, 2006, Pages 422-429

  Chow, K W ^a   Conte, Robert ^b   Xu, Neil ^c  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

^b SERVICE DE PHYSIQUE DE L ETAT CONDENSÉ   (France)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Ablowitz and Ladik model; Discrete nonlinear Schr dinger equation; Elliptic function solutions

Indexed keywords

SOLITONS;

BRIGHT SOLITONS; COMPLEX PLANES; CONTINUUM LIMITS; DINGER EQUATION; DISCRETE BREATHER; DISCRETE DARK SOLITONS; DOUBLY PERIODIC; ELLIPTIC FUNCTIONS;

NONLINEAR EQUATIONS;

EID: 29644435708     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2005.09.053     Document Type: Article

References (26)

1. M.J. Ablowitz, and J.F. Ladik J. Math. Phys. 16 1975 598
2. M.J. Ablowitz, Y. Ohta, and A.D. Trubatch Phys. Lett. A 253 1999 287
3. M. Abramowitz, and I. Stegun Handbook of Mathematical Functions tenth ed. 1972 Dover New York
4. S. Ahmad, and A.R. Chowdhury J. Phys. A 20 1987 293
5. N.N. Akhmediev, and A. Ankiewicz Phys. Rev. A 47 1993 3213
6. A.R. Bishop, G. Kalosakas, K.Ø. Rasmussen, and P.G. Kevrekidis Chaos 13 2003 588
7. N.N. Bogolyubov Jr., and A.K. Prikarpatskii Dokl. Akad. Nauk SSSR 27 1982 1103 Sov. Phys. Dokl. 27 1982 113 (in English)
8. D. Cai, A.R. Bishop, and N. Grønbech-Jensen Phys. Rev. E 52 1995 R5784
9. D. Cai, A.R. Bishop, and N. Grønbech-Jensen Phys. Rev. E 53 1996 1202
10. K.W. Chow Wave Motion 35 2002 71
11. B.C. Gupta, and S.B. Lee Phys. Lett. A 269 2000 130
12. G.-H. Halphen Traité des fonctions elliptiques et de leurs applications, Première partie, Théorie des fonctions elliptiques et de leurs développements en série 1886 Gauthier-Villars Paris 492 pages
13. R. Hirota J. Math. Phys. 14 1973 805
14. M. Johansson, and S. Aubry Phys. Rev. E 61 2000 5864
15. P.G. Kevrekidis, Y.S. Kivshar, and A.S. Kovalev Phys. Rev. E 67 2003 046604
16. Y.S. Kivshar, P.G. Kevrekidis, and S. Takeno Phys. Lett. A 307 2003 287
17. V.V. Konotop, and S. Takeno Phys. Rev. E 54 1996 2010
18. D.F. Lawden Elliptic Functions and Applications 1989 Springer-Verlag New York
19. W. Magnus, F. Oberhettinger, and R.P. Soni Formulas and Theorems for the Special Functions of Mathematical Physics third enlarged ed. 1966 Springer Berlin
20. B.A. Malomed, and J. Yang Phys. Lett. A 302 2002 163
21. K. Maruno, Y. Ohta, and N. Joshi Phys. Lett. A 311 2003 214
22. D. Mihalache, F. Lederer, and D.M. Baboiu Phys. Rev. A 47 1993 3285
23. P.D. Miller, N.M. Ercolani, I.M. Krichever, and C.D. Levermore Commun. Pure Appl. Math. 48 1996 1369
24. K. Narita J. Phys. Soc. Jpn. 59 1990 3528
25. I.E. Papacharalampous, P.G. Kevrekidis, B.A. Malomed, and D.J. Frantzeskakis Phys. Rev. E 68 2003 046604
26. V.E. Vekslerchik J. Phys. A 32 1999 4983