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

Jibin Li

doi:10.3934/dcdsb.2014.19.1719

Article Contents

2014, Volume 19, Issue 6: 1719-1729. Doi: 10.3934/dcdsb.2014.19.1719

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

Jibin Li^1,

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

Received: September 2013

Revised: February 2014

Published online: June 2014

Abstract / Introduction Related Papers Cited by

Abstract

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.

Keywords:

Generalized two-component Hunter-Saxton system,
solitary wave solution,
peakon,
periodic cusp wave solution.

Mathematics Subject Classification: Primary: 34A05, 34C25-28, 34M55, 35Q51, 35Q53; Secondary: 58F05, 58F14, 58F30.

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