Exactsolitary wave and quasi-periodic wave solutions for four fifth-ordernonlinear wave equations

Jibin Li; Yi Zhang

doi:10.3934/dcdsb.2010.13.623

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2010, Volume 13, Issue 3: 623-631. Doi: 10.3934/dcdsb.2010.13.623

This issue Previous Article Asymptotic behavior of second-order nonlinear dynamic equations on time scales Next Article Some new results on explicit traveling wave solutions of $K(m, n)$ equation

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

Jibin Li^1, and
Yi Zhang^1,

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

Received: March 31, 2009

Revised: September 30, 2009

Published: September 2010

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Abstract

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.

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Mathematics Subject Classification: 34C23, 34C37, 35Q55, 37K45, 58Z05, 74J30.

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

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