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

Authors
Plechac, P Sverak, V
Citation
P. Plechac et V. Sverak, On self-similar singular solutions of the complex Ginzburg-Landau equation, COM PA MATH, 54(10), 2001, pp. 1215-1242
Citations number
20
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
ISSN journal
00103640 → ACNP
Volume
54
Issue
10
Year of publication
2001
Pages
1215 - 1242
Database
ISI
SICI code
0010-3640(200110)54:10<1215:OSSSOT>2.0.ZU;2-Z
Abstract
We address the open problem of existence of singularities for the complex G inzburg-Landau equation. Using a combination of rigorous results and numeri cal computations, we describe a countable family of self-similar singularit ies. Our analysis includes the supercritical nonlinear Schrodinger equation as a special case. We also consider the problem of stability of these sing ularities. (C) 2001 John Wiley & Sons, Inc.