Bifurcations of Travelling Wave Solutions for the Generalized Drinfeld-Sokolov Equations

LONG Yao; RUI Wei-guo; HE Bin; CHEN Can

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LONG Yao, RUI Wei-guo, HE Bin, CHEN Can. Bifurcations of Travelling Wave Solutions for the Generalized Drinfeld-Sokolov Equations[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1357-1362.

Citation:

LONG Yao, RUI Wei-guo, HE Bin, CHEN Can. Bifurcations of Travelling Wave Solutions for the Generalized Drinfeld-Sokolov Equations[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1357-1362.

Citation:

LONG Yao, RUI Wei-guo, HE Bin, CHEN Can. Bifurcations of Travelling Wave Solutions for the Generalized Drinfeld-Sokolov Equations[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1357-1362.

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Bifurcations of Travelling Wave Solutions for the Generalized Drinfeld-Sokolov Equations

Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, P. R. China

Received Date: 2005-10-09
Rev Recd Date: 2006-08-06
Publish Date: 2006-11-15

Abstract

Abstract

Ansatz method and the theory of dynamical systems are used to the study of the traveling wave solutions for the generalized Drinfeld-Sokolov equations.Under two groups of the parametric-conditions,more solitary wave solutions,kink and anti-kink wave solutions and periodic wave solutions were obtained.Exact explicit parametric representations of these travelling wave solutions are given.
- solitary wave,
- kink wave,
- periodic wave,
- generalized Drinfeld-Sokolov equation

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References(7)

References

[1]	Gurses M,Karasu A.Integrable KdV systems: recursion operators of degree four[J].Phys Lett A,1999,251(4):247—249. doi: 10.1016/S0375-9601(98)00910-4
[2]	HU Jian-lan.A new method of exact travelling wave solution for coupled nonlinear differential equations[J].Phys Lett A,2004,325(1):37—42. doi: 10.1016/j.physleta.2004.01.074
[3]	Chow S N,Hale J K.Method of Bifurcation Theory[M].New York:Springer-Verlag,1981.
[4]	Guckenheimer J,Holmes P J.Nonlinear Oscillations，Dynamical Systems and Bifurcations of Vector Fields[M].New York:Springer-Verlag,1983.
[5]	LI Ji-bin,LIU Zheng-rong.Smooth and non-smooth travelling waves in a nonlinearly dispersive equation[J].Appl Math Modelling,2000,25(1):41—56. doi: 10.1016/S0307-904X(00)00031-7
[6]	LI Ji-bin,LIU Zheng-rong.Travelling wave solutions for a class of nonlinear dispersive equations[J].Chinese Ann Math Ser B,2003,23(3):397—418.
[7]	LONG Yao,RUI Wei-guo,HE Bin.Travelling wave solutions for a higher order wave equations of KdV type(Ⅰ)[J].Chaos Solitons and Fractals,2005,23(2):469—475. doi: 10.1016/j.chaos.2004.04.027