Traveling wave solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity

Wenjing Zhu, Yonghui Xia and Yuzhen Bai

Applied Mathematics and Computation, 2020, vol. 382, issue C

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.

Keywords: Bifurcation; Ginzburg-Landau equation; Travelling wave solution; Dynamical system (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320303088

DOI: 10.1016/j.amc.2020.125342

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