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October  2010, 26(4): 1525-1536. doi: 10.3934/dcds.2010.26.1525

A dual-Petrov-Galerkin method for two integrable fifth-order KdV type equations

Juan-Ming Yuan 1, and  Jiahong Wu 2,

1. 

Department of Financial and Computational Mathematics, Providence University, Taichung 43301, Taiwan
2. 

Department of Mathematics, Oklahoma State University, Stillwater, OK 74078

Received  November 2008 Revised  April 2009 Published  December 2009

This paper extends the dual-Petrov-Galerkin method proposed by Shen [21], further developed by Yuan, Shen and Wu [27] to general fifth-order KdV type equations with various nonlinear terms. These fifth-order equations arise in modeling different wave phenomena. The method is implemented to compute the multi-soliton solutions of two representative fifth-order KdV equations: the Kaup-Kupershmidt equation and the Caudry-Dodd-Gibbon equation. The numerical results imply that this scheme is capable of capturing, with very high accuracy, the details of these solutions such as the nonlinear interactions of multi-solitons.
Keywords: Fifth-order KdV equation, Caudrey-Dodd-Gibbon equation, Kaup-Kupershmidt equation, Dual-Petrov-Galerkin method, Multi-soliton..
Mathematics Subject Classification: Primary: 35Q53; Secondary: 65M6.
Citation: Juan-Ming Yuan, Jiahong Wu. A dual-Petrov-Galerkin method for two integrable fifth-order KdV type equations. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1525-1536. doi: 10.3934/dcds.2010.26.1525
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