# American Institute of Mathematical Sciences

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

 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.
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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