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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 716719, 19 pages
http://dx.doi.org/10.1155/2012/716719
Research Article

Symbolic Computation and the Extended Hyperbolic Function Method for Constructing Exact Traveling Solutions of Nonlinear PDEs

1School of Computer Science and Educational Software, Guangzhou University, Guangzhou 510006, China
2School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
3Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China

Received 31 May 2012; Revised 6 August 2012; Accepted 13 August 2012

Academic Editor: Renat Zhdanov

Copyright © 2012 Huang Yong 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

On the basis of the computer symbolic system Maple and the extended hyperbolic function method, we develop a more mathematically rigorous and systematic procedure for constructing exact solitary wave solutions and exact periodic traveling wave solutions in triangle form of various nonlinear partial differential equations that are with physical backgrounds. Compared with the existing methods, the proposed method gives new and more general solutions. More importantly, the method provides a straightforward and effective algorithm to obtain abundant explicit and exact particular solutions for large nonlinear mathematical physics equations. We apply the presented method to two variant Boussinesq equations and give a series of exact explicit traveling wave solutions that have some more general forms. So consequently, the efficiency and the generality of the proposed method are demonstrated.