The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 213, Issue 1-2, 1996, Pages 49-55

  Ma, W X ^a,b   Fuchssteiner, B ^b  

^a FUDAN UNIVERSITY   (China)

^b UNIVERSITY OF PADERBORN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BI-HAMILTONIAN STRUCTURES; INTEGRABLE HIERARCHY; KDV HIERARCHY; PERTURBATION EQUATION; SOLITON EQUATION;

HAMILTONIANS;

EID: 0003069487     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/0375-9601(96)00112-0     Document Type: Article

References (19)

1. R.L. Herman, J. Phys. A: Math. Gen. 23 (1990) 2327-2362.
2. Y. Matsuno, Phys. Rev. E 51 (1995) 1471-1483.
3. K.M. Tamizhmani and M. Lakshmanan, J. Phys. A: Math. Gen. 16 (1983) 3773-3782.
4. R.M. Miura, SIAM Rev. 18 (1976) 412-459.
5. M.J. Ablowitz and H. Segur, Solitons and the inverse scattering transform (SIAM, Philadelphia, 1981).
6. W.X. Ma, Acta Math. Appl. Sinica 13 (1990) 484-496.
7. B. Fuchssteiner, Nonlinear Analysis TMA 3 (1979) 849-862.
8. B. Fuchssteiner and A.S. Fokas, Physica D 4 (1981) 47-66.
9. F. Magri, J. Math. Phys. 19 (1978) 1156-1162.
10. I.M. Gel'fand and I.Y. Dorfman, Funct. Anal. Appl. 13 (1979) 248-262.
11. B. Fuchssteiner, Applications of analytic and geometric methods to nonlinear differential equations, ed. P.A. Clarkson (Kluwer, Dordrecht, 1993) p. 125-138.
12. P.J. Olver, Applications of Lie groups to differential equations, Graduate Texts in Mathematics 107 (Springer, New York, 1986).
13. R. Schmidt, Infinite dimensional Hamiltonian systems (Bibliopolis, Naples, 1987).
14. P. Casati, F. Magri and M. Pedroni, Contemp. Math. 132 (1992) 213-234.
15. G. Marmo and G. Vilasi, Phys. Lett. B 277 (1992) 137-140.
16. W. Oevel, J. Math. Phys. 29 (1988) 210-219.
17. D.J. Kaup, Nonlinear systems of partial differential equations in applied mathematics, Lectures in Applied Mathematics 23, Part 1, eds. B. Nicolaenko, D.D. Holm and J.M. Hyman (AMS, Providence, 1986) p. 195-215.
18. A.H. Nayfeh, Perturbation methods (Wiley, New York, 1973).
19. R.A. Kraenkel, M.A. Manna, J.C. Montero and J.G. Pereira, J. Math. Phys. 36 (1995) 6822-6828.