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Title

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

Shaoyong Li
Organization: School of Mathematics and Information Sciences, Shaoguan University
Zhengrong Liu
Journal / Anthology

Nonlinear Dynamics
Year: 2015
Volume: 79
Page range: 903918
Description

By using the bifurcationmethod of dynamical systems and numerical simulation approach of differential equations, we investigate generalized KdV equation ut = u2ux − u2uxxx − 4uuxuxx − (ux )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.
Subject

*Mathematics > Calculus and Analysis