Variational identities and Hamiltonian structures

AIP Conference Proceedings

Volumn 1212, Issue , 2010, Pages 1-27

  Ma, Wen Xiu ^a  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

Author keywords

Hamiltonian formalism; Integrable coupling; Lie algebra; Soliton equation; Trace identity; Variational identity

Indexed keywords

EID: 77949819380     PISSN: 0094243X     EISSN: 15517616     Source Type: Conference Proceeding    
DOI: 10.1063/1.3367042     Document Type: Conference Paper

References (78)

1. R. K. Bullough and P. J. Caudrey, Solitons, Topics in Current Physics 17, (Springer-Verlag, Berlin, 1980).
2. M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge University Press, Cambridge, 1991).
3. F. Calogero, A. Degasperis, Spectral Transform and Solitons, Vol. I, Studies in Mathematics and its Applications 13 (North-Holland Publishing Co., Amsterdam-New York, 1982).
4. L. D. Faddeev and L. A. Takhtajan, Hamiltonian Methods in the Theory of Solitons (Springer-Verlag, Berlin, 1987).
5. P. D. Lax, Comm. Pure Appl. Math. 21, 467-490 (1968).
6. W. X. Ma, X. X. Xu and Y. F. Zhang, Phys. Lett. A 351, 125-130 (2006).
7. W. X. Ma, X. X. Xu and Y. F. Zhang, J. Math. Phys. 47, 053501 (2006).
8. N. Jacobson, Lie Algebras (Interscience Publishers, New York-London, 1962).
9. W. X. Ma and B. Fuchssteiner, Chaos, Solitons & Fractals 7, 1227-1250 (1996).
10. W. X. Ma, Methods Appl. Anal. 7, 21-55 (2000).
11. B. A. Kupershmidt, J. Nonlinear Math. Phys. 8, 363-445 (2001).
12. W. X. Ma, Phys. Lett. A 316, 72-76 (2003).
13. F. K. Guo and Y. F. Zhang, Chaos, Solitons & Fractals 19, 1207-1216 (2004).
14. T. C. Xia, F. J. Yu and Y. Zhang, Phys. A 343, 238-246 (2004).
15. W. X. Ma, J. Math. Phys. 46, 033507 (2005).
16. H. Y. Ding, Y. P. Sun and X. X. Xu, Chaos, Solitons & Fractals 30, 227-234 (2006).
17. Z. Li, Y. J. Zhang and H. H. Dong, Modern Phys. Lett. B 21, 595-602 (2007).
18. Y. F. Zhang and E. G. Fan, Internat. J. Modern Phys. B 21, 3809-3824 (2007).
19. V. G. Drinfel'd and V. V. Sokolov, Soviet Math. Dokl. 23, 457-462 (1981).
20. M. A. Olshanetsky and A. M. Perelomov, Phys. Rep. C 71, 313-400 (1981).
21. M. Boiti, C. Laddomada, F. Pempinelli and G. Z. Tu, J. Math. Phys. 24, 2035-2041 (1983).
22. M. Antonowicz and A. P. Fordy, Phys. D 28, 345-357 (1987).
23. W. X. Ma and M. Pavlov, Phys. Lett. A 246, 511-522 (1998).
24. F. Calogero, Classical Many-Body Problems Amenable to Exact Treatments, Lecture Notes in Physics, New Series m: Monographs, 66 (Springer-Verlag, Berlin, 2001).
25. P. A. Clarkson and P. Winternitz, in: The Painlevé Property, 591-660, CRM Ser. Math. Phys. (Springer, New York, 1999).
26. P. Basarab-Horwath, V. Lahno and R. Zhdanov, Acta Appl. Math. 69, 43-94 (2001).
27. W. X. Ma and Z. X. Zhou, Progr. Theoret. Phys. 96, 449-457 (1996).
28. J. C. Hurtubise and E. Markman, Commun. Math. Phys. 223, 533-552 (2001).
29. W. X. Ma, Nonlinear Anal. 71, e1716-e1726 (2009).
30. G. Z. Tu, J. Phys. A: Math. Gen. 22, 2375-2392 (1989).
31. W. X. Ma, Chinese Ann. Math. Ser. A 13, 115-123 (1992).
32. X. B. Hu, J. Phys. A: Math. Gen. 27, 2497-2514 (1994).
33. W. X. Ma, in: Proceedings of CAST First Academic Annual Meeting of Youths, Science Volume, Chinese Science and Technology Press, 7-14 (1992).
34. W. X. Ma, Chinese Sci. Bull. 38, 2025-2031 (1993).
35. W. X. Ma, J. Phys. A: Math. Gen. 26, 2573-2582 (1993).
36. W. X. Ma, J. Phys. A: Math. Gen. 25, L719-L726 (1992).
37. W. X. Ma, J. Math. Phys. 33, 2464-2476 (1992).
38. Z. J. Qiao, Phys. A 252, 377-387 (1998).
39. G. Z. Tu, J. Phys. A: Math. Gen. 23, 3903-3922 (1990).
40. W. X. Ma and B. Fuchssteiner, J. Math. Phys. 40, 2400-2418 (1999).
41. D. J. Zhang and D. Y. Chen, J. Phys. A: Math. Gen. 35, 7225-7241 (2002).
42. W. X. Ma, Phys. Lett. A 179, 179-185 (1993).
43. M. Blaszak, Multi-Hamiltonian Theory of Dynamical Systems, Texts and Monographs in Physics (Springer-Verlag, Berlin, 1998).
44. W. X. Ma, J. Phys. A: Math. Theor. 40, 15055-15069 (2007).
45. W. X. Ma, J. S. He and Z. Y. Qin, J. Math. Phys. 49, 033511 (2008).
46. W. X. Ma and R. G. Zhou, in: Recent Advances in Integrable Systems (Kowloon, 2000), 106-126 (2002).
47. W. X. Ma and R. G. Zhou, Chinese Ann. Math. Ser. B 23, 373-384 (2002).
48. I. M. Gel'fand and I. Ja. Dorfman, Funktsional. Anal. i Prilozhen. 13, 13-30, 96 (1979).
49. L. A. Dickey, Soliton Equations and Hamiltonian Systems, Second edition, Advanced Series in Mathematical Physics 26 (World Scientific, River Edge, NJ, 2003).
50. G. Z. Tu, Sci. Sinica Ser. A 29, 138-148 (1986).
51. G. Z. Tu, J. Math. Phys. 30, 330-338 (1989).
52. I. D. Ido, Bull. Phys. Math. Soc. Kazan 7, 3-43 (1935).
53. L. Luo, W. X. Ma and E. G. Fan, Internat. J. Modern Phys. A 23, 1309-1325 (2008).
54. L. Luo and E. G. Fan, Sci. China Ser. A 52, 147-159 (2009).
55. W. X. Ma, J. Math. Phys. 43, 1408-1421 (2002).
56. W. X. Ma and M. Chen, J. Phys. A: Math. Gen. 39, 10787-10801 (2006).
57. W. X. Ma and Y. Zhang, Appl. Anal., to appear.
58. F. K. Guo and Y. F. Zhang, Phys. Lett. A 366, 403-410 (2007).
59. P. J. E. Peebles and B. Ratra, Rev. Modern Phys. 75, 559-606 (2003).
60. J. Hogan, Nature 448, 240-245 (2007).
61. W. X. Ma, J. Phys. Soc. Jpn. 64, 1085-1091 (1995).
62. F. Magri, J. Math. Phys. 19, 1156-1162 (1978).
63. B. Fuchssteiner and A. S. Fokas, Phys. D 4, 47-66 (1981/82).
64. B. Fuchssteiner, Nonlinear Anal. 3, 849-862 (1979).
65. W. X. Ma and X. G. Geng, Phys. Lett. B 475, 56-62 (2000).
66. K. M. Tamizhmani and M. Lakshmanan, J. Phys. A: Math. Gen. 16, 3773-3782 (1983).
67. W. X. Ma and B. Fuchssteiner, Phys. Lett. A 213, 49-55 (1996).
68. L. Frappat, A. Sciarrino and P. Sorba, Dictionary on Lie Algebras and Superalgebras (Academic Press, San Diego, CA, 2000).
69. H. Z. Sun and Q. Z. Han, Lie Algebras and Lie Superalgebras and Their Applications in Physics (Peking University Press, Beijing, 1999).
70. A. R. Chowdhury and R. Swapna, J. Math. Phys. 27, 2464-2468 (1986).
71. X. B. Hu, J. Phys. A: Math. Gen. 30, 619-32 (1997).
72. F. K. Guo and Y. F. Zhang, J. Phys. A: Math. Gen. 38, 8537-8548 (2005).
73. M. Gürses and O. Oguz, Phys. Lett. A 108, 437-40 (1985).
74. M. J. Ablowitz, D. J. Kaup, A. C. Newell and H. Segur, Stud. Appl. Math. 53, 249-315 (1974).
75. W. X. Ma and R. G. Zhou, Phys. A 296, 60-74 (2001).
76. W. X. Ma and L. Gao, Modern Phys. Lett. B 23, 1847-1860 (2009).
77. Yu. I. Manin and A. O. Radul, Comm. Math. Phys. 98, 65-77 (1985).
78. A. Nersessian, in: Supersymmetric Mechanics Vol. 1, 139-188, Lecture Notes in Phys. 698 (Springer, Berlin, 2006).