On self-similar singular solutions of the complex Ginzburg-Landau equation

Details On self-similar singular solutions of the complex Ginzburg-Landau equation On self-similar singular solutions of the complex Ginzburg-Landau equation

2000-07-25

arxiv.org/abs/math/0007149v2

Mathematics

Analysis of PDEs

23 pages, 18 figures (eps)

Scientific paper

We address the open problem of existence of singularities for the complex Ginzburg-Landau equation. Using a combination of rigourous results and numerical computations, we describe a countable family of self-similar singularities. Our analysis includes the super-critical non-linear Schroedinger equation as a special case, and most of the described singularities are new even in that situation. We also consider the problem of stability of these singularities.

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