Exact localized and periodic solutions of the Ablowitz-Ladik discrete nonlinear Schrödinger system

Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

Volumn 60, Issue 8-9, 2005, Pages 573-582

  Lai, Xian Jing ^a,b   Zhang, Jie Fang ^b  

^a ZHEJIANG SHUREN UNIVERSITY   (China)

^b ZHEJIANG NORMAL UNIVERSITY   (China)

Author keywords

Ablowitz Ladik Discrete Nonlinear Schr dinger System; Discrete Soliton; Periodic Solution

Indexed keywords

EID: 26044478890     PISSN: 09320784     EISSN: None     Source Type: Journal    
DOI: 10.1515/zna-2005-8-904     Document Type: Article

References (30)

1. P. G. Kevrekidis, K. O. Rasmussen, and A. R. Bishop, Int. J. Mod. Phys. B15, 2833 (2001).
2. A. C. Scott, Philos. Trans. R. Soc. London A315, 423 (1985).
3. A. C. Scott and L. Macneil, Phys. Lett. A98, 87 (1983).
4. A. J. Sievers and S. Takeno, Phys. Rev. Lett. 61, 970 (1988).
5. W. P. Su, J. R. Schieer, and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979).
6. P. Marquii, J. M. Bilbaut, and M. Remoissenet, Phys. Rev. E51, 6127 (1995).
7. A. Trombettoni and A. Smerzi, Phys. Rev. Lett. 86, 2353 (2001).
8. F. Lederer, S. Darmanyan, and A. Kobyakov, in: Spatial Solitons (Eds. S. Trillo and W. E. Toruellas), Springer, Berlin 2001, p. 311.
9. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
10. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
11. O. Bang and P. Miller, Opt. Lett. 21, 1105 (1996).
12. M. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
13. A. A. Sukhorukov and Y. Kivshar, Phys. Rev. E65, 036609 (2002).
14. D. N. Christodoulides and N. K. Efremidis, Opt. Lett. 27, 568 (2002);
15. K.-I. Maruno, A. Ankiewicz, and N. Akhmediev, Opt. Commun. 221, 199 (2003).
16. H. W. Tam, W. X. Ma, X. B. Hu, and D. L. Wang, J. Phys. Soc. Jpn. 69, 45 (2000).
17. E. Belokolos, A. Bobenko, V. Enol'skij, A. Its, and V. Matveev, Algebro-geometrical Approach to Nonlinear Integrable Equations, Springer-Verlag, Berlin 1994.
18. M. S. Alber and Y. N. Fedorov, Inverse Probl. 17, 1017 (2001).
19. D. P. Novikov, Math. J. 40, 136 (1999).
20. C. W. Cao, X. G. Geng, and H. Y. Wang, J. Math. Phys. 43, 621 (2002).
21. W. Malfliet, Am. J. Phys. 60, 650 (1992).
22. Yu. B. Suris, Miura Transformations for Toda-type Integrable Systems, with Applications to the Problem of Integrable Discretizations, SFB 288 Fachbereich Mathmatik, Technische Universität Berlin, Berlin 1998.
23. M. J. Ablowitz and J. F. Ladik, Stud. Appl. Math. 57, 1 (1997).
24. R. Hirota and M. Lwao, Time-discretization of soliton equation, in: SIDE III-Symmetries and Integarabiof Difference Equations (Eds. D. Levi and O. Ragnisco), CRM Proc. & Lect. Notes 25, Ams, Providence, Rhode Island 2000, pp. 217-229.
25. A. Davydov, J. Theor. Biol. 38, 559 (1973).
26. S. Takeno and G. Hori, J. Phys. Soc. Jpn. 60, 947 (1991).
27. A. Aceves, C. Angelis, G. Luther, G. Rubenchik, and S. Turitsyn, Phys. Rev. Lett. 75, 73 (1995).
28. M. J. Ablowitz and J. F. Ladik, Stud. Appl. Math. 55, 213 (1977).
29. G. R. W. Quispel, F. W. Nijhoff, H. W. Capel, and J. van der Linden, Physica A 125, 344 (1984).
30. Z. Y. Van, Chaos, Solitons and Fractals 18, 299 (2003).