Vortex rings for the Gross-Pitaevskii equation | Zendy

Fabrice Béthuel | Zendy; Giandomenico Orlandi | Zendy; Didier Smets | Zendy

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Vortex rings for the Gross-Pitaevskii equation

Author(s) -

Fabrice Béthuel,

Giandomenico Orlandi,

Didier Smets

Publication year - 2004

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/2

Subject(s) - mathematics , gross–pitaevskii equation , vortex , mathematical physics , mathematical analysis , bose–einstein condensate , quantum mechanics , physics , thermodynamics

. 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).

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