On elliptic solutions of the cubic complex one-dimensional Ginzburg-Landau equation

Abstract

The cubic complex one-dimensional Ginzburg-Landau equation is considered. Using the Hone's method, based on the use of the Laurent-series solutions and the residue theorem, we have proved that this equation has neither elliptic standing wave nor elliptic travelling wave solutions. This result amplifies the Hone's result, that this equation has no elliptic travelling wave solutions.

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References in corpus (2)

• Exact Travelling Wave Solutions of Some Nonlinear Nonlocal Evolutionary Equations
• Construction of Single-valued Solutions for Nonintegrable Systems with the Help of the Painleve Test

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• All meromorphic traveling waves of cubic and quintic complex Ginzburg-Landau equations