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Xu, Guoan; Zhang, Yi; Li, Jibin

Exact solitary wave and periodic-peakon solutions of the complex Ginzburg-Landau equation: dynamical system approach. (English) Zbl 1540.35106

Math. Comput. Simul. 191, 157-167 (2022).
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.

Cited in 4 Documents

MSC:

35C08 Soliton solutions
35Q56 Ginzburg-Landau equations
35Q53 KdV equations (Korteweg-de Vries equations)

Keywords:

complex Ginzburg-Landau equation; solitary wave solution; periodic wave solution; pseudo-peakon; periodic peakon; compacton family

Software:

ATFM
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Full Text: DOI

References:

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