JournalsjemsVol. 6 , No. 1DOI 10.4171/jems/2

Vortex rings for the Gross-Pitaevskii equation

  • Didier Smets

    UPMC, Université Paris 06, France
  • Giandomenico Orlandi

    Università di Verona, Italy
  • Fabrice Bethuel

    Université Pierre et Marie Curie, Paris, France
Vortex rings for the Gross-Pitaevskii equation cover

Abstract

We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross-Pitaevskii (GP) equation in dimension N3.N\geq 3. 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 N=3N=3).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 N=3N=3).