Journal of Applied Mathematics
Volume 2012 (2012), Article ID 363879, 25 pages
http://dx.doi.org/10.1155/2012/363879
Research Article

Periodic Wave Solutions and Their Limits for the Generalized KP-BBM Equation

Ming Song1,2 and Zhengrong Liu1

1Department of Mathematics, South China University of Technology, Guangzhou 510640, China
2Department of Mathematics, Faculty of Sciences, Yuxi Normal University, Yuxi 653100, China

Received 17 April 2012; Accepted 15 May 2012

Academic Editor: Junjie Wei

Copyright © 2012 Ming Song 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 use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain periodic wave solutions, kink wave solutions, unbounded wave solutions, blow-up wave solutions, and solitary wave solutions.