# American Institute of Mathematical Sciences

August  2014, 19(6): 1719-1729. doi: 10.3934/dcdsb.2014.19.1719

## Bifurcations and exact travelling wave solutions of the generalized two-component Hunter-Saxton system

 1 Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004

Received  September 2013 Revised  February 2014 Published  June 2014

In this paper, we apply the method of dynamical systems to a generalized two-component Hunter-Saxton system. Through qualitative analysis, we obtain bifurcations of phase portraits of the traveling system. Under different parameter conditions, exact explicit smooth solitary wave solutions, solitary cusp wave solutions, as well as periodic wave solutions are obtained. To guarantee the existence of these solutions, rigorous parametric conditions are given.
Citation: Jibin Li. Bifurcations and exact travelling wave solutions of the generalized two-component Hunter-Saxton system. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1719-1729. doi: 10.3934/dcdsb.2014.19.1719
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