Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation

Abstract

We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie's lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method.

14 pages, no figure, to appear, Acta Applicandae Mathematicae

References in corpus (3)

• Explicit expressions for meromorphic solution of autonomous nonlinear ordinary differential equations
• Meromorphic solutions of a third order nonlinear differential equation
• Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation

Cited by in corpus (4)

• New solutions to the complex Ginzburg-Landau equations
• Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation
• All meromorphic traveling waves of cubic and quintic complex Ginzburg-Landau equations
• Degenerate elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation