Exact solitary wave and quasi-periodic wave solutions for four fifth-order nonlinear wave equations

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May 2010, 13(3): 623-631. doi: 10.3934/dcdsb.2010.13.623

Exact solitary wave and quasi-periodic wave solutions for four fifth-order nonlinear wave equations

1.	Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China

Received April 2009 Revised October 2009 Published February 2010

Abstract
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The paper is devoted to four kinds of fifth-order nonlinear wave equations including the Caudrey-Dodd-Gibbon equation, Kupershmidt equation, Kaup-Kupershmidt equation and Sawada-Kotera equation. The exact soliton solution and quasi-periodic solutions are found by using Cosgrove's work and the method of dynamical systems. The geometrical explanations of these solutions are also discussed. To guarantee the existence of the above solutions, the parameter conditions are determined.

Keywords: integrable system, quasi-periodic solution, nonlinear wave equation, soliton solution, 4-dimensional dynamical system..

Mathematics Subject Classification: 34C23, 34C37, 35Q55, 37K45, 58Z05, 74J3.

Citation: Jibin Li, Yi Zhang. Exact solitary wave and quasi-periodic wave solutions for four fifth-order nonlinear wave equations. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 623-631. doi: 10.3934/dcdsb.2010.13.623

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