Traveling wave solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity. (English) Zbl 1508.35171
Summary: 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.
MSC:
| 35Q56 | Ginzburg-Landau equations |
| 35C07 | Traveling wave solutions |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
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