English

A generalized Complex Ginzburg-Landau Equation: global existence and stability results

Analysis of PDEs 2020-11-09 v2

Abstract

We consider the complex Ginzburg-Landau equation with two pure-power nonlinearities and a damping term. After proving a general global existence result, we focus on the existence and stability of several periodic orbits, namely the trivial equilibrium, bound-states and solutions independent of the spatial variable. In particular, we construct bound-states either explicitly in the real line or through a bifurcation argument for a double eigenvalue of the Dirichlet-Laplace operator on bounded domains.

Keywords

Cite

@article{arxiv.1905.08521,
  title  = {A generalized Complex Ginzburg-Landau Equation: global existence and stability results},
  author = {Simão Correia and Mário Figueira},
  journal= {arXiv preprint arXiv:1905.08521},
  year   = {2020}
}