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Exact solitary wave and periodic-peakon solutions of the complex Ginzburg–Landau equation: Dynamical system approach

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  • Xu, Guoan
  • Zhang, Yi
  • Li, Jibin

Abstract

Using the bifurcation theory of the planar dynamical system, we study the exact solutions of the complex Ginzburg–Landau equation which is a popular model in mathematical physics. All possible exact explicit parametric representations of traveling wave solutions are given under different parameter conditions, including the solitary wave solutions, periodic wave solutions, compacton solutions pseudo-peakon solutions and periodic peakon solutions. In more general parametric conditions, all possible solutions are caught in one dragnet.

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  • 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.
    • Handle: RePEc:eee:matcom:v:191:y:2022:i:c:p:157-167
    DOI: 10.1016/j.matcom.2021.08.007
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    References listed on IDEAS

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