Calculus of Variations and Geometric Measure Theory
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F. Bethuel - G. Orlandi - D. Smets

Vortex rings for the Gross-Pitaevskii equation

created on 06 Jun 2003
modified on 20 Feb 2004


Published Paper

Inserted: 6 jun 2003
Last Updated: 20 feb 2004

Journal: J. Eur. Math. Soc.
Volume: 6
Number: 1
Pages: 17-94
Year: 2004


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

Keywords: Non linear Schroedinger equation, travelling waves, prescribed curvature equation


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