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Article Dans Une Revue Nonlinear Analysis: Theory, Methods and Applications Année : 2014

Standing waves of the complex Ginzburg-Landau equation

Résumé

We prove the existence of nontrivial standing wave solutions of the complex Ginzburg-Landau equation $\phi_t = e^{i\theta} \Delta \phi + e^{i\gamma} |\phi |^\alpha \phi $ with periodic boundary conditions. Our result includes all values of $\theta $ and $\gamma $ for which $\cos \theta \cos \gamma >0$, but requires that $\alpha >0$ be sufficiently small.

Dates et versions

hal-00906995 , version 1 (20-11-2013)

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Thierry Cazenave, Flávio Dickstein, Fred B. Weissler. Standing waves of the complex Ginzburg-Landau equation. Nonlinear Analysis: Theory, Methods and Applications, 2014, 103, pp.26. ⟨10.1016/j.na.2014.03.001⟩. ⟨hal-00906995⟩
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