Two types of new Lie algebras and corresponding hierarchies of evolution equations

Chaos, Solitons and Fractals

Volumn 23, Issue 3, 2005, Pages 1033-1041

  Xia, Tiecheng ^a,b   Chen, Xiaohong ^b   Chen, Dengyuan ^a  

^a SHANGHAI UNIVERSITY   (China)

^b BOHAI UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; HAMILTONIANS; HIERARCHICAL SYSTEMS; INTEGRAL EQUATIONS; NONLINEAR EQUATIONS; NUMBER THEORY; PROBLEM SOLVING; SET THEORY;

EVOLUTION EQUATION HIERARCHY; ISOSPECTRAL PROBLEMS; LIE ALGEBRA;

SOLITONS;

EID: 4644307508     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(04)00361-3     Document Type: Article

References (34)

1. Ablowitz MJ, Clarkson PA. Solitons, nonlinear evolution equations and inverse scattering. Cambridge: Cambridge University Press; 1991.
2. Newell AC. Soliton in mathematics and physics. Philadelphia: SIAM; 1985.
3. Wadati M. J Phys Soc Jpn 1972;32:1681.
4. Wadati M. J Phys Soc Jpn 1973;34:1289-96.
5. Wadati M, Sanuki H, Konno K. Prog Theor Phys 1975;53:419-36.
6. Tu GZ. J Math Phys 1989;30:330-7.
7. Fan EG. J Phys A: Math Gen 2001;34:513-9.
8. Yan ZY, Zhang HQ. Chaos Solitons & Fractals 2002;13:1439-50; Chaos Solitons & Fractals 2002; 14:1445-56; Chaos Solitons & Fractals 2002;14:441-6.
9. Yan ZY, Zhang HQ. Chaos Solitons & Fractals 2002;13:1439-50; Chaos Solitons & Fractals 2002; 14:1445-56; Chaos Solitons & Fractals 2002;14:441-6.
10. Yan ZY, Zhang HQ. Chaos Solitons & Fractals 2002;13:1439-50; Chaos Solitons & Fractals 2002; 14:1445-56; Chaos Solitons & Fractals 2002;14:441-6.
11. Yan ZY. Chaos Solitons & Fractals 2003; 15:639-45.
12. Fan EG. Physica A 2001;301:105-10.
13. Fan EG. J Math Phys 2000;41:7769-78.
14. Tsuchida T, Wadati M. Chaos Solitons & Fractals 1998;9:869-73.
15. Ma WX. Chaos Solitons & Fractals 1996;7:1227-50.
16. Ma WX. J Math Ann 1992; 13:115-23 [in Chinese].
17. Ma WX, Zhou RG. A coupled AKNS-Kaup-Newell soliton hierarchy. J Math Phys 1999;40:4419-28.
18. Zhang YF. Chaos Solitons & Fractals 2003;18:855-62; Chaos Solitons & Fractals 2004;21:305-10.
19. Zhang YF. Chaos Solitons & Fractals 2003;18:855-62; Chaos Solitons & Fractals 2004;21:305-10.
20. Zhang YF, Yan QY. Chaos Solitons & Fractals 2004;21:413-23.
21. Xu XX. Chaos Solitons & Fractals 2003;15:475-86.
22. Cao CW. Sci China Ser A 1990;33:528-36.
23. Geng XG. J Math Phys 1993;34:805-17.
24. Zeng YB. Phys Lett A 1991;160:541-7.
25. Zeng YB, Hietarinta J. Classical Possion structure and r-matrice from constrained flow. J Phys A 1996;29:5241-51.
26. Qiao Zhijun. A Bargmann system and the involutive representation of solutions of the Levi hierarchy. J Phys A 1993;26:4407-17.
27. Tiecheng Xia, Xiaohong Chen, Dengyuan Chen. A Lax integrable hierarchy, bi-Hamiltonian structure and finite-dimensional Liouville integrable involutive systems. Chaos Solitons & Fractals 2004;22:939-45.
28. Tiecheng Xia, Xiaohong Chen, Dengyuan Chen. A new Lax integrable hierarchy, N Hamiltonian structure and its integrable couplings system. Chaos Solitons & Fractals, in press.
29. Fuchssteiner B. Coupling of completely integrable system: the perturbation bundle. In: Clarkson PA, editor. Applications of analytic and geometric method to nonlinear differential equations. Dordrecht: Kluwer; 1993. p. 125-38.
30. Lakshtnanan M, Tamizhmani KM. J Math Phys 1985;26:1189-200.
31. Ma W, Fuchsteiner B. Chaos, Solitons & Fractals 1996;7:1227-50.
32. Yufeng Zhang. Phys Lett A 2003;310:19-24.
33. Yufeng Zhang, Zhang H. J Math Phys 2002;43:466-72.
34. Yufeng Zhang, Zhang H. Phys Lett A 2002;299:543-8.