On a class of spatial discretizations of equations of the nonlinear Schrödinger type

Mathematics and Computers in Simulation

Volumn 74, Issue 4-5, 2007, Pages 343-351

  Kevrekidis, P G ^a,c   Dmitriev, S V ^b,c   Sukhorukov, A A ^b,c  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

^b INSTITUTE OF INDUSTRIAL SCIENCE   (Japan)

^c AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING; THEOREM PROVING;

CONSERVATION LAWS; CONTINUUM SIBLINGS; DISCRETIZATIONS; LATTICE MOMENTUM; SCHRODINGER (NLS) EQUATIONS;

NONLINEAR EQUATIONS;

EID: 33847123911     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2006.10.014     Document Type: Article

References (37)

1. Ablowitz M.J., and Ladik J.F. J. Math. Phys. 16 (1975) 598
2. Ablowitz M.J., and Ladik J.F. J. Math. Phys. 17 (1976) 1011
3. Ablowitz M.J., Herbst B.M., and Schober C. J. Comp. Phys. 126 (1993) 299
4. Aubry S. Physica D 103 (1997) 201
5. Flach S., and Willis C.R. Phys. Rep. 295 (1998) 181
6. Hennig D., and Tsironis G. Phys. Rep. 307 (1999) 333
7. Barashenkov I.V., Oxtoby O.F., and Pelinovsky D.E. Phys. Rev. E 72 (2005) 035602R
8. Oxtoby O.F., Pelinovsky D.E., and Barashenkov I.V. Nonlinearity 19 (2006) 217
9. Bender C.M., and Tovbis A. J. Math. Phys. 38 (1997) 3700
10. Christodoulides D.N., Lederer F., and Silberberg Y. Nature 424 (2003) 817
11. Kivshar Yu.S., and Agrawal G.P. Optical Solitons: From Fibers to Photonic Crystals (2003), Academic Press, San Diego
12. Dmitriev S.V., Kevrekidis P.G., Sukhorukov A.A., Yoshikawa N., and Takeno S. Phys. Lett. A 356 (2006) 324
13. Dmitriev S.V., Kevrekidis P.G., and Yoshikawa N. J. Phys. A 38 (2005) 7617
14. Dmitriev S.V., Kevrekidis P.G., and Yoshikawa N. J. Phys. A 39 (2006) 7217
15. Dmitriev S.V., Kevrekidis P.G., Yoshikawa N., and Frantzeskakis D.J. Phys. Rev. E 74 (2006) 046609
16. Efremidis N.K., and Christodoulides D.N. Phys. Rev. E 65 (2002) 056607
17. Kevrekidis P.G., et al. Physica D 183 (2003) 87
18. Gómez-Gardenes J., Falo F., and Floría L.M. Phys. Lett. A 332 (2004) 213
19. Gómez-Gardenes J., Floría L.M., Peyrard M., and Bishop A.R. Chaos 14 (2004) 1130
20. Hadziewski L., et al. Phys. Rev. Lett. 93 (2004) 033901
21. Kapitula T., and Kevrekidis P.G. Nonlinearity 14 (2001) 533
22. Kevrekidis P.G. Physica D 183 (2003) 68
23. Kevrekidis P.G., and Frantzeskakis D.J. Mod. Phys. Lett. B 18 (2004) 173
24. Kevrekidis P.G., et al. Mod. Phys. Lett. B 18 (2004) 1481
25. Konotop V.V., and Brazhnyi V.A. Mod. Phys. Lett. B 18 (2004) 627
26. Kevrekidis P.G., Rasmussen K.O., and Bishop A.R. Int. J. Mod. Phys. B 15 (2001) 2833
27. Orfanidis S.J. Phys. Rev. D 18 (1978) 3828
28. Öster M., Johansson M., and Eriksson A. Phys. Rev. E 67 (2003) 056606
29. Pilloni L., and Levi D. Phys. Lett. A 92 (1982) 5
30. Pelinovsky D.E. Nonlinearity 19 (2006) 2695
31. Pelinovsky D.E., and Rothos V.M. Physica D 202 (2005) 16
32. Peyrard M. Nonlinearity 17 (2004) R1
33. Peyrard M., and Kruskal M. Physica D 14 (1984) 88
34. Salerno M. Phys. Rev. A 46 (1992) 6856
35. Speight J.M. Nonlinearity 12 (1999) 1373
36. Speight J.M., and Ward R.S. Nonlinearity 7 (1994) 475
37. Speight J.M., and Zolotaryuk Y. Nonlinearity 19 (2006) 1365