Abstract Employing the bifurcation theory of planar dynamical system, we study the bifurcations and exact solutions of the complex Ginzburg-Landau equation. All possible explicit representations of travelling wave solutions are given 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. Finally, we conclude our main results in a theorem at the end of the paper.

中文翻译：

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具有克尔定律非线性的复Ginzburg-Landau方程的行波解

摘要 利用平面动力系统的分岔理论，研究了复Ginzburg-Landau方程的分岔和精确解。给出了不同参数区域下所有可能的行波解的显式表示，包括压缩波解、扭结和反扭结波解、孤立波解、周期波解等。有趣的是，行驶系统的第一积分随参数而变化。因此，相图将随着参数的变化而变化。最后，我们在论文末尾的定理中总结了我们的主要结果。