On self-similar singular solutions of the complex Ginzburg-Landau equation
Analysis of PDEs
2007-05-23 v2 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.math/0007149,
title = {On self-similar singular solutions of the complex Ginzburg-Landau equation},
author = {Petr Plechac and Vladimir Sverak},
journal= {arXiv preprint arXiv:math/0007149},
year = {2007}
}
Comments
23 pages, 18 figures (eps)