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

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 c...

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Bibliographic Details
Published inMathematics and computers in simulation Vol. 191; pp. 157 - 167
Main Authors Xu, Guoan, Zhang, Yi, Li, Jibin
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2022
Subjects
Compacton family
Complex Ginzburg–Landau equation
Periodic peakon
Periodic wave solution
Pseudo-peakon
Solitary wave solution
Pseudo-peakon
Periodic peakon
Periodic wave solution
Solitary wave solution
Compacton family
Complex Ginzburg–Landau equation
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Summary: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.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2021.08.007