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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 812120, 14 pages
http://dx.doi.org/10.1155/2013/812120
Research Article

Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation

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

Received 15 July 2013; Accepted 16 September 2013

Academic Editor: Hagen Neidhardt

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.

Abstract

We study the bifurcation phenomena of nonlinear waves described by a generalized Zakharov-Kuznetsov equation . We reveal four kinds of interesting bifurcation phenomena. The first kind is that the low-kink waves can be bifurcated from the symmetric solitary waves, the 1-blow-up waves, the tall-kink waves, and the antisymmetric solitary waves. The second kind is that the 1-blow-up waves can be bifurcated from the periodic-blow-up waves, the symmetric solitary waves, and the 2-blow-up waves. The third kind is that the periodic-blow-up waves can be bifurcated from the symmetric periodic waves. The fourth kind is that the tall-kink waves can be bifurcated from the symmetric periodic waves.