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Journal of Applied Mathematics
Volume 2013, Article ID 490341, 17 pages
http://dx.doi.org/10.1155/2013/490341
Research Article

The Traveling Wave Solutions and Their Bifurcations for the BBM-Like Equations

1College of Mathematics and Information Sciences, Shaoguan University, Shaoguan, Guangdong 512005, China
2Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, China

Received 3 June 2013; Accepted 3 July 2013

Academic Editor: Shiping Lu

Copyright © 2013 Shaoyong Li and Zhengrong Liu. 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

We investigate the traveling wave solutions and their bifurcations for the BBM-like equations by using bifurcation method and numerical simulation approach of dynamical systems. Firstly, for BBM-like equation, we obtain some precise expressions of traveling wave solutions, which include periodic blow-up and periodic wave solution, peakon and periodic peakon wave solution, and solitary wave and blow-up solution. Furthermore, we reveal the relationships among these solutions theoretically. Secondly, for BBM-like equation, we construct two periodic wave solutions and two blow-up solutions. In order to confirm the correctness of these solutions, we also check them by software Mathematica.