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

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  • Zhu, Wenjing
  • Xia, Yonghui
  • Bai, Yuzhen

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.

Suggested Citation

  • Zhu, Wenjing & Xia, Yonghui & Bai, Yuzhen, 2020. "Traveling wave solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    • Handle: RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320303088
    DOI: 10.1016/j.amc.2020.125342
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    References listed on IDEAS

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    1. Zhang, Bei & Xia, Yonghui & Zhu, Wenjing & Bai, Yuzhen, 2019. "Explicit exact traveling wave solutions and bifurcations of the generalized combined double sinh–cosh-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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    Cited by:

    1. Xu, Guoan & Zhang, Yi & Li, Jibin, 2022. "Exact solitary wave and periodic-peakon solutions of the complex Ginzburg–Landau equation: Dynamical system approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 157-167.

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