A note on dark solitons in nonlinear complex Ginzburg-Landau equations

Abstract

We analyze the existence of dark solitons in nonlinear complex Ginzburg-Landau equations. We prove existence results concerned with the initial value problem for these equations in Zhidkov spaces using a new approach with splitting methods. MSC 2010. 47J35.

A Note on the Well-Posedness of Control Complex Ginzburg-Landau Equations in Zhidkov Spaces

“…It describes a large number of linear and nonlinear phenomena from superconductivity, superfluidity and Bose-Einstein condensation to liquid crystals [1]. Well-posedness of (1.1) has been studied with different nonlinearities and in different spaces (see for instance, [4,11,12]). Our aim is to study the well-posedness of the Complex Ginzburg-Landau equation with a bilinear control term, in Zhidkov spaces, using splitting methods.…”

“…The goal of this article is to prove well-posedness of (1.1) for Zhidkov spaces in the real line, using splitting the result in [4]. These are numerical methods that split the flow of the equation, to approximate solutions.…”

Polynomial Complex Ginzburg-Landau equations in almost periodic spaces

“…We use splitting-methods for evolution equations developed for numerical purposes [12], [10]. These methods were used to prove well-posedness of Complex Ginzburg-Landau equations and Reaction-diffusion equations in other spaces [7], [8], [6], [5].…”