Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 597431, 17 pages
Research Article

Bifurcation of Traveling Wave Solutions for a Two-Component Generalized -Equation

School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

Received 19 October 2012; Accepted 20 November 2012

Academic Editor: Ezzat G. Bakhoum

Copyright © 2012 Zhenshu Wen. 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.


We study the bifurcation of traveling wave solutions for a two-component generalized -equation. We show all the explicit bifurcation parametric conditions and all possible phase portraits of the system. Especially, the explicit conditions, under which there exist kink (or antikink) solutions, are given. Additionally, not only solitons and kink (antikink) solutions, but also peakons and periodic cusp waves with explicit expressions, are obtained.