American Institute of Mathematical Sciences

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October  1999, 5(4): 871-880. doi: 10.3934/dcds.1999.5.871

Bifurcating vortex solutions of the complex Ginzburg-Landau equation

Hans G. Kaper 1, and  Peter Takáč 2,

1. 

Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, United States
2. 

Fachbereich Mathematik, Universität Rostock, Universitätsplatz 1, D-18055 Rostock

Received  December 1998 Revised  June 1999 Published  July 1999

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.
Keywords: bifurcation, Complex Ginzburg-Landau equation, determining nodes., vortex solutions.
Mathematics Subject Classification: 35K55, 35Q35, 58F1.
Citation: Hans G. Kaper, Peter Takáč. Bifurcating vortex solutions of the complex Ginzburg-Landau equation. Discrete & Continuous Dynamical Systems, 1999, 5 (4) : 871-880. doi: 10.3934/dcds.1999.5.871
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