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MiS Preprint
48/2000

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

Petr Plechac and Vladimír Šverák

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 Schrödinger 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.

Received:
Aug 10, 2000
Published:
Aug 10, 2000
MSC Codes:
35Q55
Keywords:
ginzburg-landau equation, nonlinear schrödinger equation, singularities

Related publications

inJournal
2001 Repository Open Access
Petr Plechac and Vladimír Šverák

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

In: Communications on pure and applied mathematics, 54 (2001) 10, pp. 1215-1242