Table of Contents
Journal of Nonlinear Dynamics
Volume 2014, Article ID 468392, 5 pages
Research Article

Exact Solitary Wave Solution in the ZK-BBM Equation

College of Science, Beijing University of Chemical Technology, Beijing 100029, China

Received 16 June 2014; Revised 4 August 2014; Accepted 18 August 2014; Published 31 August 2014

Academic Editor: Giovanni P. Galdi

Copyright © 2014 Juan Zhao and Wei 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.


The traveling wave solution for the ZK-BBM equation is considered, which is governed by a nonlinear ODE system. The bifurcation structure of fixed points and bifurcation phase portraits with respect to the wave speed c are analyzed by using the dynamical system theory. Furthermore, the exact solutions of the homoclinic orbits for the nonlinear ODE system are obtained which corresponds to the solitary wave solution curve of the ZK-BBM equation.