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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 148132, 9 pages
http://dx.doi.org/10.1155/2014/148132
Research Article

New Exact Solutions for a Higher Order Wave Equation of KdV Type Using Multiple -Expansion Methods

Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, China

Received 16 February 2014; Accepted 9 April 2014; Published 29 April 2014

Academic Editor: Giorgio Kaniadakis

Copyright © 2014 Yinghui He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The -expansion method is a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems. In our work, exact traveling wave solutions of a generalized KdV type equation of neglecting the highest order infinitesimal term, which is an important water wave model, are discussed by the -expansion method and its variants. As a result, many new exact solutions involving parameters, expressed by Jacobi elliptic functions, hyperbolic functions, trigonometric function, and the rational functions, are obtained. These methods are more effective and simple than other methods and a number of solutions can be obtained at the same time. The related results are enriched.