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Abstract and Applied Analysis
Volume 2014, Article ID 189486, 20 pages
http://dx.doi.org/10.1155/2014/189486
Research Article

Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d-Sokolov System

Department of Mathematics, South China University of Technology, Guangzhou 510640, China

Received 29 March 2014; Accepted 28 May 2014; Published 7 July 2014

Academic Editor: Chun-Lei Tang

Copyright © 2014 Huixian Cai et al. 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

We study the bifurcations of nonlinear waves for the generalized Drinfel’d-Sokolov system called system. We reveal some interesting bifurcation phenomena as follows. (1) For system, the fractional solitary waves can be bifurcated from the trigonometric periodic waves and the elliptic periodic waves, and the kink waves can be bifurcated from the solitary waves and the singular waves. (2) For system, the compactons can be bifurcated from the solitary waves, and the peakons can be bifurcated from the solitary waves and the singular cusp waves. (3) For system, the solitary waves can be bifurcated from the smooth periodic waves and the singular periodic waves.