Bifurcating vortex solutions of the complex Ginzburg-Landau equation
Hans G. Kaper, Peter Takac
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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