Dynamics of vortices for the complex Ginzburg–Landau equation

Miot, Evelyne

doi:10.2140/apde.2009.2.159

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Dynamics of vortices for the complex Ginzburg–Landau equation

Evelyne Miot

Vol. 2 (2009), No. 2, 159–186

DOI: 10.2140/apde.2009.2.159

Abstract

We study a complex Ginzburg–Landau equation in the plane, which has the form of a Gross–Pitaevskii equation with some dissipation added. We focus on the regime corresponding to well-prepared unitary vortices and derive their asymptotic motion law.

Keywords

complex Ginzburg–Landau equation, vortex dynamics

Mathematical Subject Classification 2000

Primary: 35B20, 35B40, 35Q40, 82D55

Milestones

Received: 21 October 2008

Accepted: 27 March 2009

Published: 1 May 2009

Authors

Evelyne Miot
Laboratoire J.-L. Lions UMR 7598 Université Pierre et Marie Curie 175 rue du Chevaleret 75013 Paris France

Vol. 2, No. 2, 2009