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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 704931, 15 pages
http://dx.doi.org/10.1155/2012/704931
Research Article

Extension on Bifurcations of Traveling Wave Solutions for a Two-Component Fornberg-Whitham Equation

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

Received 20 September 2012; Accepted 16 November 2012

Academic Editor: Zhenya Yan

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.

Abstract

Fan et al. studied the bifurcations of traveling wave solutions for a two-component Fornberg-Whitham equation. They gave a part of possible phase portraits and obtained some uncertain parametric conditions for solitons and kink (antikink) solutions. However, the exact explicit parametric conditions have not been given for the existence of solitons and kink (antikink) solutions. In this paper, we study the bifurcations for the two-component Fornberg-Whitham equation in detalis, present all possible phase portraits, and give the exact explicit parametric conditions for various solutions. In addition, not only solitons and kink (antikink) solutions, but also peakons and periodic cusp waves are obtained. Our results extend the previous study.