Nonlinear Schrödinger family on moving space curves: Lax Pairs, soliton solution and equivalent spin chain

Chaos, Solitons and Fractals

Volumn 9, Issue 10, 1998, Pages 1709-1722

  Porsezian, K ^a,b  

^a Leibniz University Hannover   (Germany)

^b ANNA UNIVERSITY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRATION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; SOLITONS;

CONTINUUM SPIN CHAINS; EQUIVALENT SPIN CHAIN; HASHIMOTO THEORY; LAX PAIRS; NONLINEAR SCHRODINGER (NLS) EQUATIONS; SPACE CURVE FORMALISM; VORTEX FILAMENT MOTION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0032183267     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(97)00132-X     Document Type: Article

References (47)

1. Ablowitz, M. J., Kaup, D. J., Newell, A. C., Segur, H., Stud. Appl. Math. Phys., 1974, 53, 249.
2. Ablowitz, M. J., Ramani, A., Segur, H., J. Math. Phys., 1980, 27, 1006.
3. Lamb, G. L., Elements of Soliton Theory. John Wiley and Sons, New York, 1980.
4. Haldane, F. D. M., Opt. Lett., 1986, 11, 730.
5. Lakshmanan, M., Phys. Lett. A, 1977, 61, 53.
6. Belavin, A. A., Polyakov, A. M., JETP Lett., 1975, 22, 245.
7. Balakrishnan, R., Bishop, A. R., Dandoloff, R., Phys. Rev. Lett., 1990, 64, 2107.
8. Lamb, G. L., J. Math. Phys., 1977, 18, 1654.
9. Hasimoto, H., J. Fluid Mech., 1972, 51, 477.
10. Zubusky, N. J., Kruskal, M. D., Phys. Rev. Lett., 1965, 15, 240.
11. Cieslinski, J., Phys. Lett. A, 1990, 149, 139.
12. Lakshmanan, M., Ganesan, S., Phys. A, 1985, 132, 117.
13. Daniel, M., Porsezian, K., Lakshmanan, M., J. Math. Phys., 1994, 35, 6498.
14. Porsezian, K., Tamizhmani, K. M., Lakshmanan, M., Phys. Lett. A, 1987, 124, 159.
15. Porsezian, K., Daniel, M., Lakshmanan, M., J. Math. Phys., 1992, 33, 1807.
16. Porsezian, K., Lakshmanan, M., J. Math. Phys., 1992, 32, 2923.
17. Porsezian, K., Phys. Rev. E, 1997, 55, 3785.
18. Balakrishnan, R., Partha, Guha, J. Math. Phys., 1996, 37, 3651.
19. Beower, R. C., Kessler, D. A., Koplik, J., Levine, H., Phys. Rev. A, 1984, 29, 1335.
20. Lund, F., Regge, T., Phys. Rev. D, 1976, 14, 1524.
21. Goldstein, R. E., Petrich, D. M., Phys. Rev. Lett., 1991, 67, 3203;
22. Goldstein, R. E., Petrich, D. M., Phys. Rev. Lett., 1991, 69, 555.
23. Nakayama, K., Segur, H., Wadati, M., Phys. Rev. Lett., 1992, 69, 2603.
24. Doliwa, A., Santini, P. M., Phys. Lett. A, 1994, 185, 373.
25. Uby, L., Isichenko, M. B., Yankov, V. V., Phys. Rev. E, 1995, 52, 932.
26. Kaup, D. J., Newell, A. C., J. Math. Phys., 1978, 19, 798.
27. Wadati, M., Kono, K., Ichikawa, Y., J. Phys. Soc. Japan, 1979, 46, 1965.
28. Hasegawa, A., Tappert, F. D., Appl. Phys. Lett., 1973, 23, 142.
29. Ablowitz, M. J. and Segur, H., Solitons and Inverse Scattering Transform. SIAM, Philadelphia, 1981.
30. Zakharov, V. L, Takhtajan, L. A., Teoret. Mat. Fiz., 1979, 61, 118.
31. Zabolotskii, A. A., Phys. Lett. A, 1987, 124, 500.
32. Kundu, A., J. Phys. A, 1987, 20, 1107.
33. Kundu, A., J. Math. Phys., 1984, 25, 3433.
34. Kundu, A., J. Phys. A, 1986, 19, 1303.
35. Kodama, Y., J. Stat. Phys., 1985, 39, 597.
36. Porsezian, K., Nakkeeran, K., Phys. Rev. Lett., 1996, 76, 3955.
37. Sasa, S., Satsuma, J., J. Phys. Soc. Japan, 1991, 60, 409.
38. Uby, L., Proc. Roy. Soc. London Ser. A, 1996, 452, 1531.
39. Abdulleav, F., Theory of Solitons in Inhomogeneous Media. John Wiley and Sons, New York, 1994.
40. Chen, H. H., Liu, C. S., Phys. Fluids, 1978, 21, 377.
41. Porsezian, K., Pramana, 1997, 48, 143.
42. Lakshmanan, M., Bullough, R. K., Phys. Lett. A, 1980, 80, 287.
43. Balakrishnan, R., Phys. Lett. A, 1982, 92, 243.
44. Belic, M. R., J. Phys. A, 1985, 18, L409.
45. Lakshmanan, M., Daniel, M., Phys. A, 1981, 107, 533.
46. Ruijgrok, Th. W., Jurkiewicz, J., Phys. A, 1980, 103, 573.
47. Weiss, J., Tabor, M., Carnevale, G., J. Math. Phys., 1983, 24, 532.