Bifurcating vortex solutions of the complex Ginzburg-Landau equation

Details Bifurcating vortex solutions of the complex Ginzburg-Landau equation Bifurcating vortex solutions of the complex Ginzburg-Landau equation

1999-06-25

arxiv.org/abs/math/9906172v1

Mathematics

Dynamical Systems

To appear in Discrete and Continuous Dynamical Systems (1999); 10 pages, 2 figures

Scientific paper

It is shown that the complex Ginzburg-Landau (CGL) equation on the real line admits nontrivial $2\pi$-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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