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arXiv · 1301.5526

Standing waves of the complex Ginzburg-Landau equation

Thierry Cazenave·Flávio Dickstein·Fred B. Weissler
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Abstract

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.

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Thierry Cazenave, Flávio Dickstein, Fred B. Weissler. 2013-01-23. Standing waves of the complex Ginzburg-Landau equation. https://doi.org/10.1016/j.na.2014.03.001

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