Traveling wave solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity
作者：
Highlights：
• All possible explicit representations of travelling wave solutions are given for Ginzburg-Landau under different parameter regions, including compactons, kink and anti-kink wave solutions, solitary wave solutions, periodic wave solutions and so on.
• It is interesting that first integral of the travelling system changes with respect to the parameters. Consequently, the phase portraits will change with respect to the changes of parameters.
• This paper presents a method to investigate exact traveling wave solutions and bifurcations of the complex Ginzburg-Landau equation based on applying the bifurcation theory of planar dynamical systems.
• Our main results on bifurcation of travelling wave are presented at the end of the paper.
摘要
•All possible explicit representations of travelling wave solutions are given for Ginzburg-Landau under different parameter regions, including compactons, kink and anti-kink wave solutions, solitary wave solutions, periodic wave solutions and so on.•It is interesting that first integral of the travelling system changes with respect to the parameters. Consequently, the phase portraits will change with respect to the changes of parameters.•This paper presents a method to investigate exact traveling wave solutions and bifurcations of the complex Ginzburg-Landau equation based on applying the bifurcation theory of planar dynamical systems.•Our main results on bifurcation of travelling wave are presented at the end of the paper.
论文关键词：Bifurcation,Ginzburg-Landau equation,Travelling wave solution,Dynamical system
论文评审过程：Received 17 January 2020, Revised 1 April 2020, Accepted 26 April 2020, Available online 13 May 2020, Version of Record 13 May 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125342
