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Abstract and Applied Analysis
Volume 2015, Article ID 820916, 14 pages
http://dx.doi.org/10.1155/2015/820916
Research Article

Bifurcation of Traveling Wave Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy

1College of Applied Science, Beijing University of Technology, Beijing 100124, China
2School of Mathematics and Statistics, Tianshui Normal University, Tianshui, Gansu 741001, China

Received 27 June 2014; Accepted 15 July 2014

Academic Editor: Yonghui Xia

Copyright © 2015 Yanping Ran 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

Four (2+1)-dimensional nonlinear evolution equations, generated by the Jaulent-Miodek hierarchy, are investigated by the bifurcation method of planar dynamical systems. The bifurcation regions in different subsets of the parameters space are obtained. According to the different phase portraits in different regions, we obtain kink (antikink) wave solutions, solitary wave solutions, and periodic wave solutions for the third of these models by dynamical system method. Furthermore, the explicit exact expressions of these bounded traveling waves are obtained. All these wave solutions obtained are characterized by distinct physical structures.