一维复Ginzburg-Landau方程的分岔及其精确行波解

Bifurcation and Exact Traveling Wave Solutions for the One-dimensional Complex Ginzburg-Landau Equation

利用动力系统分岔理论,研究了一维复Ginzburg-Landau(CGL)方程的分岔及其精确行波解.通过行波变换将非线性发展方程转化为二维平面动力系统,利用定性分析的方法,得到了该系统在不同参数条件下的所有分岔相图.借助非线性偏微分方程的行波解与对应的常微分方程的轨道的关系,通过行波系统的首次积分,获得了一维CGL方程的所有有界行波解的显示参数表达式.

Using bifurcation theory from dynamical systems, the bifurcation and exact traveling wave solutions for the one-dimen- sional complex Ginzburg-Landau （CGL） equation were researched. The nonlinear evolution equation was transformed to planar dy- namical system through traveling wave transformation,and qualitative analysis were preformed to the system.With the help of the relationship between the traveling wave solutions of the partial differential equation and the orbits of the corresponding ordinary dif- ferential equation, all bifurcation of phase portraits under different parameter conditions were obtained.The explicit parameter expres- sions of all types of bounded traveling wave solutions were given from the first integral of the traveling wave system.