Geodesic
Vortex rings for the Gross-Pitaevskii equation
Journal of the European Mathematical Society, Tome 6 (2004) no. 1, pp. 17-94.

Voir la notice de l'article provenant de la source EMS Press

We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross-Pitaevskii (GP) equation in dimension N≥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).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).
DOI : 10.4171/jems/2
Classification : 35-XX, 49-XX, 53-XX, 58-XX
Keywords: NLS, Gross-Pitaevskii, Ginzburg-Landau, Vortex rings 
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     title = {Vortex rings for the {Gross-Pitaevskii} equation},
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Fabrice Bethuel; Giandomenico Orlandi; Didier Smets. Vortex rings for the Gross-Pitaevskii equation. Journal of the European Mathematical Society, Tome 6 (2004) no. 1, pp. 17-94. doi : 10.4171/jems/2. http://geodesic.mathdoc.fr/articles/10.4171/jems/2/

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