Electron. J. Diff. Equ., Vol. 2014 (2014), No. 145, pp. 1-15.

Bifurcation of traveling wave solutions of a generalized K(n,n) equation

Xiaoshan Zhao, Guanhua Zhao, Linping Peng

In this article, a generalized K(n,n) equation is studied by the qualitative theory of bifurcations and the method of dynamical systems. The result shows the existence of the different kinds of traveling solutions of the generalized K(n,n) equation, including solitary waves, kink waves, periodic wave and compacton solutions, which depend on different parametric ranges. Moreover, various sufficient conditions to guarantee the existence of the above traveling solutions are provided under different parameters conditions.

Submitted March 14, 2013. Published June 20, 2014.
Math Subject Classifications: 34C25-28, 35B08, 35B10, 35B40.
Key Words: Solitary wave; periodic wave; kink wave; compatons; bifurcation.

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Xiaoshan Zhao
School of Science
Tianjin University of Technology and Education
Tianjin 300222, China
email: xszhao678@126.com
Guanhua Zhao
Department of Mathematics, Handan College
Handan, Hebei 056005, China
email: zghlds@126.com
Linping Peng
School of Mathematics and System Sciences
Beihang University, LIMB of the Ministry of Education
Beijing 100191, China
email: penglp@buaa.edu.cn

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