On the NLS dynamics for infinite energy vortex configurations on the plane
type: Item
instance of: scholarly article
title: On the NLS dynamics for infinite energy vortex configurations on the plane
zbMATH Open document ID: 1180.35045
DOI: 10.4171/RMI/552
author: Fabrice Béthuel
author: Didier Smets
author: Robert L. Jerrard
published in: Revista Matemática Iberoamericana
publication date: 2008-11-05T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1218475359
full work available at URL: https://eudml.org/doc/42391
review text: The aim of this paper is to study the dynamics of vortices for the nonlinear Schrödinger equation on the plane, when the total degree at infinity is nonzero. The equation which the authors are interested in is written on \(\mathbb{R}^2\times\mathbb{R}\) as \[ i\partial_tu_\varepsilon+\Delta u_\varepsilon=\frac{1} {\varepsilon^2}\left(| u_\varepsilon|^2-1\right)\cdot u_\varepsilon,\tag{1} \] where \(0<\varepsilon<1\) denotes a small parameter. The authors derive the asymptotical dynamical law.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35B20
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 82D50
zbMATH DE Number: 5361879
zbMATH Keywords: vortex dynamics
zbMATH Keywords: NLS equation
zbMATH Keywords: superfluids
MaRDI profile type: Publication
cites work: Threshold transition energies for Ginzburg-Landau functionals
cites work: On uniqueness of vector-valued minimizers of the Ginzburg-Landau functional in annular domains
cites work: Ginzburg-Landau vortices
cites work: Small energy solutions to the Ginzburg–Landau equation
cites work: Dynamics of multiple degree Ginzburg-Landau vortices
cites work: A remark on the Cauchy problem for the 2D Gross-Pitaevskii equation with nonzero degree at infinity.
cites work: BOUNDARY PROBLEMS FOR THE GINZBURG–LANDAU EQUATION
cites work: Q4212659
cites work: The Jacobian and the Ginzburg-Landau energy
cites work: Refined Jacobian estimates for Ginzburg-Landau functionals
cites work: Refined Jacobian estimates and Gross-Pitaevsky vortex dynamics
cites work: Some properties of solutions of the Ginzburg-Landau equation on an open set of \(\mathbb{R}^ 2\)
cites work: On the incompressible fluid limit and the vortex motion law of the nonlinear Schrödinger equation
cites work: Q4715861
description: scientific article; zbMATH DE number 5361879