A family of completely integrable multi-Hamiltonian systems explicitly related to some celebrated equations

Journal of Mathematical Physics

Volumn 42, Issue 9, 2001, Pages 4327-4344

  Fan, Engui ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035537190     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1389288     Document Type: Article

References (42)

1. M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Phys Rev. Lett. 31, 125 (1973).
2. A. C. Newell, Salitons in Mathematics and Physics (SIAM, Philadelphia, PA, 1985).
3. C. H. Gu, H. S Hu, and Z. X. Zhou, Darboux Transformation in Soliton Theory and its Geometric Applications (Shanghai Scientific and Technical Publishers, Shanghai, 1999).
4. M. Wadati, K. Konno, and Y. H. Ichikawa, J. Phys. Soc. Jpn. 47, 1698 (1979).
5. M. Boiti, F. Pempinelli, and G. Z. Tu, Prog. Theor. Phys. 69, 48 (1985).
6. D. J. Kaup and A. C. Newell, J. Math. Phys. 19, 798 (1978).
7. T. Tsuchida and M. Wadati, Phys. Lett. A 257, 53 (1999).
8. W. X. Ma, J. Phys. A 31, 7585 (1998).
9. G. Z. Tu, J. Math. Phys. 30, 330 (1989).
10. G. Z. Tu, J. Phys. A 22, 2375 (1989).
11. F. Magri, J. Math. Phys. 19, 1156 (1978).
12. F. Magri, Lectures Notes in Phys. (Springer, Berlin, 1980), Vol. 120.
13. P. J. Olver, Applications of Lie Groups to Differential Equations (Springer, New York, 1986).
14. I. M. Gel'fand and I. Y. Dorfman, Funct. Anal. Appl. 15, 173 (1981).
15. Y. Nutku, J. Math. Phys. 28, 2579 (1987).
16. C. W. Cao, Sci. China A 33, 528 (1990).
17. C. W. Cao and X. G. Geng, in Nonlinear Physics, Research Reports in Physics, edited by C. H. Gu, Y. S. Li, and G. Z. Tu (Springer, Berlin, 1990), pp. 68-78.
18. C. W. Cao and X. G. Geng, J. Phys. A 23, 4117 (1990).
19. Z. J. Qiao, J. Phys. A 26, 4407 (1993).
20. Y. B. Zeng, Phys. Lett. A 160, 541 (1991).
21. V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons (Springer-Verlag, Berlin, 1991).
22. G. Neugebauer and D. Kramer, J. Phys. A 16, 1927 (1983).
23. G. Neugebauer and R. Meinel, Phys. Lett. A 100, 467 (1984).
24. D. Levi, Inverse Probl. 4, 165 (1988).
25. Z. X. Zhou, Lett. Math. Phys. 16, 9 (1988).
26. C. H. Gu, Lett. Math. Phys. 35, 61 (1995).
27. J. Cieslinski, J. Math. Phys. 36, 5670 (1995).
28. P. G. Esteevez, J. Math. Phys. 40, 1406 (1999).
29. H. H. Chen, Y. C. Lee, and C. S. Liu, Phys. Scr. 20, 490 (1979).
30. F. Calogero and W. Eckhaus, Inverse Probl. 3, 229 (1987).
31. V. S. Gerdjikov and M. I. Ivanov, Bulg. J. Phys. 10, 130 (1983).
32. S. Kakei, N. Sasa, and J. Satsuma, J. Phys. Soc. Jpn. 64, 1519 (1995).
33. A. Kundu, Physica D 25, 399 (1987).
34. A. Kundu, J. Math. Phys. 25, 3433 (1984).
35. M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge U. P., Cambridge, 1991).
36. M. Wadati and K. Sogo, J. Phys. Soc. Jpn. 52, 394 (1983).
37. P. A. Clarkson and C. M. Cosgrove, J. Phys. A 20, 2003 (1987).
38. E. G. Fan, J. Math. Phys. 41, 7769 (2000).
39. P. J. Olver, J. Math. Phys. 18, 1212 (1977).
40. Z. Y. Yang, J. Phys. A 27, 2837 (1994).
41. V. V. Gudkov, J. Math. Phys. 38, 4794 (1997).
42. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, Berlin, 1978).