Nonlinear Dynamics

, Volume 79, Issue 2, pp 903–918 | Cite as

Kink-like wave and compacton-like wave solutions for generalized KdV equation

  • Shaoyong Li
  • Zhengrong Liu
Original Paper


By using the bifurcation method of dynamical systems and numerical simulation approach of differential equations, we investigate generalized KdV equation \(u_t=u^{2}u_{x}-u^{2}u_{xxx}-4uu_xu_{xx}-(u_x)^3\). Two types of bounded traveling wave solutions are found, that is, the kink-like wave and compacton-like wave solutions. The planar graphs of these solutions are simulated by using software Mathematica; meanwhile, some interesting phenomena are revealed, that is, under some conditions, the periodic wave can become the kink-like wave and compacton-like wave, respectively, and the solitary wave can become the kink-like wave. The exact kink-like wave and compacton-like wave solutions with implicit or parameter expressions are given.


Generalized KdV equation Kink-like wave Compacton-like wave Periodic wave Solitary wave 



All authors wish to thank the editor and the anonymous referee for many valuable suggestions leading to an improvement of this paper. This work is supported by the Science Foundation of Shaoguan University (201320501), National Natural Science Foundation of China (11401448).


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of Mathematics and Information SciencesShaoguan UniversityShaoguanPeople’s Republic of China
  2. 2.Department of MathematicsSouth China University of TechnologyGuangzhouPeople’s Republic of China

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