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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 301645, 7 pages
http://dx.doi.org/10.1155/2013/301645
Research Article

New Exact Solitary Wave Solutions of a Coupled Nonlinear Wave Equation

School of Science, Guizhou Minzu University, Guiyang, Guizhou 550025, China

Received 24 July 2013; Accepted 13 September 2013

Academic Editor: Ziemowit Popowicz

Copyright © 2013 XiaoHua Liu and CaiXia 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

By using the theory of planar dynamical systems to a coupled nonlinear wave equation, the existence of bell-shaped solitary wave solutions, kink-shaped solitary wave solutions, and periodic wave solutions is obtained. Under the different parametric values, various sufficient conditions to guarantee the existence of the above solutions are given. With the help of three different undetermined coefficient methods, we investigated the new exact explicit expression of all three bell-shaped solitary wave solutions and one kink solitary wave solutions with nonzero asymptotic value for a coupled nonlinear wave equation. The solutions cannot be deduced from the former references.