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On self‐similar singular solutions of the complex Ginzburg‐Landau equation
Author(s) -
Plecháč Petr,
Šverák Vladimír
Publication year - 2001
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3006
Subject(s) - gravitational singularity , mathematics , countable set , computation , nonlinear system , stability (learning theory) , mathematical analysis , pure mathematics , physics , computer science , algorithm , quantum mechanics , machine learning
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. © 2001 John Wiley & Sons, Inc.