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

Simão Correia; Mário Figueira

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arXiv · 1905.08521

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

Simão Correia·Mário Figueira

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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.

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Simão Correia, Mário Figueira. 2020-11-06. A generalized Complex Ginzburg-Landau Equation: global existence and stability results. https://arxiv.org/abs/1905.08521

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