Geodesic
Vortex rings for the Gross-Pitaevskii equation
Journal of the European Mathematical Society, Tome 6 (2004) no. 1, pp. 17-94 Cet article a éte moissonné depuis la source EMS Press

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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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     author = {Fabrice Bethuel and Giandomenico Orlandi and Didier Smets},
     title = {Vortex rings for the {Gross-Pitaevskii} equation},
     journal = {Journal of the European Mathematical Society},
     pages = {17--94},
     year = {2004},
     volume = {6},
     number = {1},
     doi = {10.4171/jems/2},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/2/}
}
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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

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