Bifurcations of Travelling Wave Solutions in Variant Boussinesq Equations

YUAN Yu-bo; PU Dong-mei; LI Shu-min

Volume 27 Issue 6

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Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(6): 716-726

YUAN Yu-bo, PU Dong-mei, LI Shu-min. Bifurcations of Travelling Wave Solutions in Variant Boussinesq Equations[J]. Applied Mathematics and Mechanics, 2006, 27(6): 716-726.

Citation:

YUAN Yu-bo, PU Dong-mei, LI Shu-min. Bifurcations of Travelling Wave Solutions in Variant Boussinesq Equations[J]. Applied Mathematics and Mechanics, 2006, 27(6): 716-726.

Citation:

YUAN Yu-bo, PU Dong-mei, LI Shu-min. Bifurcations of Travelling Wave Solutions in Variant Boussinesq Equations[J]. Applied Mathematics and Mechanics, 2006, 27(6): 716-726.

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Bifurcations of Travelling Wave Solutions in Variant Boussinesq Equations

1.
School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China;

Received Date: 2003-12-20
Rev Recd Date: 2006-03-06
Publish Date: 2006-06-15

Abstract

Abstract

The bifurcations of solitary waves and kink waves for variant Boussinesq equations were studied by using the bifurcation theory of planar dynamical systems.The bifurcation sets and the numbers of solitary waves and kink waves for the variant Boussinesq equations are presented.Several types explicit formulas of solitary wave solutions and kink wave solutions are obtained.In the end, several formulas of periodic wave solutions are presented.
- Hamiltonian system,
- Boussinesq equation,
- bifurcation,
- solitary wave solution,
- kink wave solutions

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References(9)

References

[1]	LI Ji-bin,ZHANG Li-jun.Bifurcations of travelling wave solutions in generalized Pochhammer-Chree equation[J].Chaos,Solitons and Fractals,2002,14(4):581—593. doi: 10.1016/S0960-0779(01)00248-X
[2]	LI Ji-bin,LIU Zheng-rong.Travelling wave solutions for a class of nonlinear dispersive equations[J].Chinese Ann Math,Ser B,2002,23(3):397—418. doi: 10.1142/S0252959902000365
[3]	张解放.变更Boussinesq方程和Kupershmidt方程的多孤子解[J].应用数学和力学，2000,21(2):171—175.
[4]	YAN Zhen-ya,ZHANG Hong-qing.New explicit and exact travelling wave solutions for a system of the variant Boussinesq equations in mathematical physics[J].Physics Letters A,1999,252(6):291—296. doi: 10.1016/S0375-9601(98)00956-6
[5]	WANG Ming-liang.Solitary wave solutions of variant Boussinesq equations[J].Physics Letters A,1995,199(3):169—172. doi: 10.1016/0375-9601(95)00092-H
[6]	Andronov A ,Leontovich E A,Gordon I I，et al.Theory of Bifurcations of Dynamic Systems on a Plane[M].New York:Wiley,1973.
[7]	Chow S N,Hale J K.Method of Bifurcation Theory[M].New York:Springer-Verlag, 1981.
[8]	Debnath L.Nonlinear Partial Differential Equations for Scientists and Engineers[M].Boston:Birkhauser, 1997.
[9]	Guckenheimer J,Holmes P J.Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields[M].New York:Springer-Verlag,1983.

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