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Bifurcating vortex solutions of the complex Ginzburg-Landau equation

Hans G. Kaper·Peter Takac
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Abstract

It is shown that the complex Ginzburg-Landau (CGL) equation on the real line admits nontrivial $2π$-periodic vortex solutions that have $2n$ simple zeros (``vortices'') per period. The vortex solutions bifurcate from the trivial solution and inherit their zeros from the solution of the linearized equation. This result rules out the possibility that the vortices are determining nodes for vortex solutions of the CGL equation.

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Hans G. Kaper, Peter Takac. 1999-06-25. Bifurcating vortex solutions of the complex Ginzburg-Landau equation. https://arxiv.org/abs/math/9906172

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