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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 379109, 10 pages
http://dx.doi.org/10.1155/2014/379109
Research Article

Bifurcation Analysis and Different Kinds of Exact Travelling Wave Solutions of a Generalized Two-Component Hunter-Saxton System

1Department of Physics, Honghe University, Mengzi, Yunnan 661100, China
2College of Mathematics, Honghe University, Mengzi, Yunnan 661100, China

Received 22 March 2014; Accepted 27 May 2014; Published 18 June 2014

Academic Editor: Hagen Neidhardt

Copyright © 2014 Qing Meng and Bin He. 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

This paper focuses on a generalized two-component Hunter-Saxton system. From a dynamic point of view, the existence of different kinds of periodic wave, solitary wave, and blow-up wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given. Also, some exact parametric representations of the travelling waves are presented.