Vortex rings for the Gross-Pitaevskii equation
Fabrice Bethuel
Université Pierre et Marie Curie, Paris, FranceGiandomenico Orlandi
Università di Verona, ItalyDidier Smets
UPMC, Université Paris 06, France
![Vortex rings for the Gross-Pitaevskii equation cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-6-issue-1.png&w=3840&q=90)
Abstract
We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross-Pitaevskii (GP) equation in dimension We also extend the asymptotic analysis of the free field Ginzburg-Landau equation to a larger class of equations, including the Ginzburg-Landau equation for superconductivity as well as the traveling wave equation for GP. In particular we rigorously derive a curvature equation for the concentration set (i.e. line vortices if ).Ginzburg-Landau equation to a larger class of equations, including the Ginzburg-Landau equation for superconductivity as well as the traveling wave equation for GP. In particular we rigorously derive a curvature equation for the concentration set (i.e. line vortices if ).
Cite this article
Fabrice Bethuel, Giandomenico Orlandi, Didier Smets, Vortex rings for the Gross-Pitaevskii equation. J. Eur. Math. Soc. 6 (2004), no. 1, pp. 17–94
DOI 10.4171/JEMS/2