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MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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