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

Petr Plecháč, Vladimír Šverák

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We address the open problem of existence of singularities for the complex Ginzburg-Landau equation. Using a combination of rigorous results and numerical computations, we describe a countable family of self-similar singularities. Our analysis includes the supercritical nonlinear Schrödinger equation as a special case. We also consider the problem of stability of these singularities.

Original languageEnglish (US)
Pages (from-to)1215-1242
Number of pages28
JournalCommunications on Pure and Applied Mathematics
Volume54
Issue number10
DOIs
StatePublished - Oct 2001

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