A study of a new class of discrete nonlinear Schrödinger equations

Journal of Physics A: Mathematical and General

Volumn 35, Issue 38, 2002, Pages 8109-8133

  Kundu, K ^a  

^a INSTITUTE OF PHYSICS   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037184146     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/35/38/312     Document Type: Article

References (76)

1. Drazin P G and Johnson R S 1989 Solitons: An Introduction (Cambridge: Cambridge University Press)
2. Scott A 1999 Nonlinear Science: Emergence and Dynamics of Coherent Structures (Oxford: Oxford University Press)
3. See e.g. Remoissenet M 1996 Waves Called Solitons: Concepts and Experiments (Berlin: Springer)
4. Kivshar Yu S and Malomed B A 1989 Rev. Mod. Phys. 63 761
5. Sagdeev R Z, Meiseev S S, Tur A V and Yanevskii V V 1986 Nonlinear Phenomena in Plasma Physics and Hydrodynamics ed R Z Sagdeev (Moscow: Mir) p 137
6. Ablowitz M J and Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)
7. Ablowitz M J and Ladik J L 1975 J. Math. Phys. 16 598 Ablowitz M J and Ladik J L 1976 J. Math. Phys. 17 1011
8. Ablowitz M J and Ladik J L 1975 J. Math. Phys. 16 598 Ablowitz M J and Ladik J L 1976 J. Math. Phys. 17 1011
9. Takeno S and Homma S 1991 J. Phys. Soc. Japan 60 731
10. Laedke E W, Spatschek K H and Turitsyn S K 1994 Phys. Rev. Lett. 73 1055
11. Ghosh A, Gupta B C and Kundu K 1998 J. Phys.: Condens. Matter 10 2701
12. Kundu K and Gupta B C 1998 Eur. Phys. J. B 3 23 Gupta B C and Kundu K 2002 Nonlinear Dynamics: Integrabilty and Chaos ed M Daniel, K M Tamizhmani and R Sahadevan (New Delhi: Narosa) p 193
13. Kundu K and Gupta B C 1998 Eur. Phys. J. B 3 23 Gupta B C and Kundu K 2002 Nonlinear Dynamics: Integrabilty and Chaos ed M Daniel, K M Tamizhmani and R Sahadevan (New Delhi: Narosa) p 193
14. Claude Ch, Kivshar Y S, Kluth O and Spatchek K H 1993 Phys. Rev. B 47 14228
15. Aceves A B, De Angelis C, Peschel T, Muschall R, Lederer F, Trillo S and Wabnitz S 1996 Phys. Rev. E 53 1172
16. Scott A C 1982 Phys. Rev. A 26 578
17. Yomosa S 1983 J. Phys. Soc. Japan 52 1866
18. Kundu K 2000 Phys. Rev. E 61 5839
19. Vakhnenko A A and Gaididei Yu B 1986 Teor. Mat. Fiz. 68 350 (Engl. transl. 1987 Theor. Math. Phys. 68 873)
20. Takeno S 1992 J. Phys. Soc. Japan 61 1433
21. Hori K and Takeno S 1992 J. Phys. Soc. Japan 61 4263
22. Konptop V V and Takeno S 1997 Phys. Rev. B 55 11342 Konotop V V and Takeno S 1998 Physica D 113 261
23. Konptop V V and Takeno S 1997 Phys. Rev. B 55 11342 Konotop V V and Takeno S 1998 Physica D 113 261
24. Kivshar Yu S, Pelinovsky D E, Cretegny T and Peyard M 1998 Phys. Rev. Lett. 80 5032
25. Davydov A S 1980 Zh. Eksp. Teor. Fiz. 78 789 (Engl. transl. 1980 Sov. Phys.-JETP 51 397)
26. Davydov A S 1980 Zh. Eksp. Teor. Fiz. 78 789 (Engl. transl. 1980 Sov. Phys.-JETP 51 397)
27. Bolterauer H 1990 Davydov's Soliton Revisited, Self-Trapping of Vibrational Energy in Protein ed P L Christiansen and A C Scott (NATO ASI Series vol 234) p 309
28. Förner W and Ladik J 1990 Davydov's Soliton Revisited, Self-Trapping of Vibrational Energy in Protein ed P L Christiansen and A C Scott (NATO ASI Series vol 234) p 267
29. Dmitriev S V, Kivshar Yu S and Shigenari T 2001 Phys. Rev. Lett. 64 056613
30. Cai D, Bishop A R and Grønbech-Jensen N 1994 Phys. Rev. Lett. 72 591
31. Johansson M and Kivshar Yu S 1999 Phys. Rev. Lett. 82 85
32. Zhou C, He X T and Chen S 1992 Phys. Rev. A 46 2277
33. Bullough R K and Caudrey P J 1980 Topics in Current Physics: Solitons ed R K Bullough and P J Caudrey (Berlin: Springer) p 6
34. Aubry S 1976 J. Chem. Phys. 64 3392
35. Kudryavtsev A E 1975 Pis. Zh. Eksp. Teor. Fiz. 22 178 (Engl. transl. 1975 JETP Lett. 22 82)
36. Kudryavtsev A E 1975 Pis. Zh. Eksp. Teor. Fiz. 22 178 (Engl. transl. 1975 JETP Lett. 22 82)
37. Getmanov B S 1976 Pis. Zh. Eksp. Teor. Fiz. 24 323 (Engl. transl. 1976 JETP Lett. 24 291)
38. Getmanov B S 1976 Pis. Zh. Eksp. Teor. Fiz. 24 323 (Engl. transl. 1976 JETP Lett. 24 291)
39. Anninos P, Oliveira S and Matzner R A 1991 Phys. Rev. D 44 1147
40. Yang J and Tan Yu 2000 Phys. Rev. Lett. 85 3624 Yang J and Tan Yu 2001 Phys. Lett. A 280 129 Tan Yu and Yang J 2001 Phys. Rev. E 64 056616
41. Yang J and Tan Yu 2000 Phys. Rev. Lett. 85 3624 Yang J and Tan Yu 2001 Phys. Lett. A 280 129 Tan Yu and Yang J 2001 Phys. Rev. E 64 056616
42. Yang J and Tan Yu 2000 Phys. Rev. Lett. 85 3624 Yang J and Tan Yu 2001 Phys. Lett. A 280 129 Tan Yu and Yang J 2001 Phys. Rev. E 64 056616
43. Friesecke G and Wattis J A D 1994 Commun. Math. Phys. 161 391
44. Toda M 1981 Theory of Nonlinear Lattices Springer (Series in Solid-State Sciences vol 20) (Berlin: Springer)
45. Friesecke G and Pego R L 1999 Nonlinearity 12 1601 Friesecke G and Pego R L 2002 Nonlinearity 15 1343
46. Friesecke G and Pego R L 1999 Nonlinearity 12 1601 Friesecke G and Pego R L 2002 Nonlinearity 15 1343
47. Marin J L and Aubry S 1996 Nonlinearity 9 1501
48. Marin J L, Aubry S and Floria L M 1998 Physica D 113 283
49. Cretegny T, Livi R and Spicci M 1998 Physica D 119 88
50. Cretegny T, Dauxois T, Ruffo S and Torcini A 1998 Physica D 121 109
51. Aubry S and Cretegny T 1998 Physica D 119 34
52. Bang O and Peyard M 1996 Phys. Rev. E 53 4143
53. Dunlap D H, Wu H-L and Phillips P 1990 Phys. Rev. Lett. 65 88
54. Kundu K, Giri D and Ray K 1996 J. Phys. A: Math Gen. 29 5699
55. Kivshar Y S and Campbell D K 1993 Phys. Rev. E 48 3077
56. Takeno S 1990 Davydov's Soliton Revisited, Self-Trapping of Vibrational Energy in Protein ed P L Christiansen and A C Scott (NATO ASI Series vol 234) p 31
57. Stegeman G I and Segev M 1999 Science 286 1518 Segev M and Stegeman G 1998 Phys. Today 51 42
58. Stegeman G I and Segev M 1999 Science 286 1518 Segev M and Stegeman G 1998 Phys. Today 51 42
59. Kanna T and Lakshmanan M 2001 Phys. Rev. Lett. 86 5043 Anastassiou C, Segev M, Steiglitz K, Giordmaine J A and Mitchell M 1999 Phys. Rev. Lett. 83 2332
60. Kanna T and Lakshmanan M 2001 Phys. Rev. Lett. 86 5043 Anastassiou C, Segev M, Steiglitz K, Giordmaine J A and Mitchell M 1999 Phys. Rev. Lett. 83 2332
61. Salerno M 1992 Phys. Rev. A 46 6856
62. Konotop V V and Salerno M 1997 Phys. Rev. E 55 4706 Konotop V V and Salerno M 1997 Phys. Rev. E 56 3611
63. Konotop V V and Salerno M 1997 Phys. Rev. E 55 4706 Konotop V V and Salerno M 1997 Phys. Rev. E 56 3611
64. Davydov A S and Kislukha N I 1976 Zh. Eksp. Tear. Fiz. 71 1090 (Engl. transl. 1976 Sov. Phys.-JETP 44 571)
65. Davydov A S and Kislukha N I 1976 Zh. Eksp. Tear. Fiz. 71 1090 (Engl. transl. 1976 Sov. Phys.-JETP 44 571)
66. Rashba E I 1982 Excitons ed E I Rashba and M D Sturge (Amsterdam: North-Holland)
67. Toyozawa Y 1983 Molecular Aggregates (Springer Series in Solid-State Sciences vol 49) ed P Reineker, H Haken and H C Wolf (Berlin: Springer)
68. van Amerongen H, Valkunas L and van Grondelle R 2000 Photosynthetic EXCITONS (Singapore: World Scientific) chapter 6 pp 197-240
69. Kaup D I 1976 SIAM J. Appl. Math. 31 121
70. Drazin P G 1992 Nonlinear Systems (Cambridge: Cambridge University Press)
71. Alligood K T, Sauer T D and Yorke J A 1997 Chaos: An Introduction to Dynamical Systems (New York: Springer)
72. Arrowsmith D K and Place C M 1982 Ordinary Differential Equations (London: Chapman and Hall)
73. Flach S, Kladko K and MacKay R 1997 Phys. Rev. Lett. 78 1207
74. Campbell D K and Peyrard M 1990 Chaos ed D K Campbell (New York: AIP) p 305
75. Cretegny T, Aubry S and Flach S 1998 Physica D 119 73
76. Das A 1989 Integrate Models (Singapore: World Scientific)