1999/06/25 by Hans G. Kaper, Peter Takáč, Kaper, Hans G. +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #math.DS #msc:35K55 #msc:35Q35 #msc:58F14
paper · pdf · doi:10.48550/arxiv.math/9906172
To appear in Discrete and Continuous Dynamical Systems (1999); 10 pages, 2 figures
arxiv created 1999/06/25 · arxiv updated 2009/11/30
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.