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Abstract and Applied Analysis
Volume 2013, Article ID 483492, 18 pages
Research Article

New Types of Nonlinear Waves and Bifurcation Phenomena in Schamel-Korteweg-de Vries Equation

1Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, China
2Department of Mathematics and Computer Science, Guizhou Normal University, Guiyang, Guizhou 550001, China

Received 26 April 2013; Accepted 3 July 2013

Academic Editor: Chuanzhi Bai

Copyright © 2013 Yun Wu and Zhengrong Liu. 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.


We study the nonlinear waves described by Schamel-Korteweg-de Vries equation . Two new types of nonlinear waves called compacton-like waves and kink-like waves are displayed. Furthermore, two kinds of new bifurcation phenomena are revealed. The first phenomenon is that the kink waves can be bifurcated from five types of nonlinear waves which are the bell-shape solitary waves, the blow-up waves, the valley-shape solitary waves, the kink-like waves, and the compacton-like waves. The second phenomenon is that the periodic-blow-up wave can be bifurcated from the smooth periodic wave.