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Abstract and Applied Analysis
Volume 2014, Article ID 153139, 9 pages
http://dx.doi.org/10.1155/2014/153139
Research Article

Bifurcation of Traveling Wave Solutions of the Dual Ito Equation

Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Received 9 May 2014; Accepted 15 July 2014; Published 5 August 2014

Academic Editor: Yonghui Xia

Copyright © 2014 Xinghua Fan and Shasha Li. 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

The dual Ito equation can be seen as a two-component generalization of the well-known Camassa-Holm equation. By using the theory of planar dynamical system, we study the existence of its traveling wave solutions. We find that the dual Ito equation has smooth solitary wave solutions, smooth periodic wave solutions, and periodic cusp solutions. Parameter conditions are given to guarantee the existence.