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Mathematical Problems in Engineering
Volume 2013, Article ID 769187, 7 pages
http://dx.doi.org/10.1155/2013/769187
Research Article

An Extended Auxiliary Function Method and Its Application in mKdV Equation

1Department of Mathematics, North University of China, Taiyuan 030051, China
2Software School, North University of China, Taiyuan 030051, China
3School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received 29 November 2012; Accepted 22 February 2013

Academic Editor: Farzad Khani

Copyright © 2013 Yafeng Xiao et al. 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

An extended auxiliary function method is presented for constructing exact traveling wave solutions to nonlinear partial differential equations. The main idea of this method is to take full advantage of the solutions to the elliptic equation to construct exact traveling wave solutions for nonlinear partial differential equations. mKdV equation is chosen to illustrate the application of the extended auxiliary function method. Consequently, more new exact traveling wave solutions are derived that are not obtained by the previously known methods.