Standing waves of the complex Ginzburg-Landau equation

Abstract

We prove the existence of nontrivial standing wave solutions of the complex Ginzburg-Landau equation ${\varphi }_t=e^{i\theta }\Delta \varphi +e^{i\gamma }|\varphi {|}^{\alpha }\varphi$ 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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