# Vortex rings for the Gross-Pitaevskii equation

Fabrice Bethuel; G. Orlandi; Didier Smets

Journal of the European Mathematical Society (2004)

- Volume: 006, Issue: 1, page 17-94
- ISSN: 1435-9855

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topBethuel, Fabrice, Orlandi, G., and Smets, Didier. "Vortex rings for the Gross-Pitaevskii equation." Journal of the European Mathematical Society 006.1 (2004): 17-94. <http://eudml.org/doc/277427>.

@article{Bethuel2004,

abstract = {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 $N=3$).},

author = {Bethuel, Fabrice, Orlandi, G., Smets, Didier},

journal = {Journal of the European Mathematical Society},

keywords = {NLS; Gross-Pitaevskii; Ginzburg-Landau; Vortex rings; finite energy solutions},

language = {eng},

number = {1},

pages = {17-94},

publisher = {European Mathematical Society Publishing House},

title = {Vortex rings for the Gross-Pitaevskii equation},

url = {http://eudml.org/doc/277427},

volume = {006},

year = {2004},

}

TY - JOUR

AU - Bethuel, Fabrice

AU - Orlandi, G.

AU - Smets, Didier

TI - Vortex rings for the Gross-Pitaevskii equation

JO - Journal of the European Mathematical Society

PY - 2004

PB - European Mathematical Society Publishing House

VL - 006

IS - 1

SP - 17

EP - 94

AB - 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 $N=3$).

LA - eng

KW - NLS; Gross-Pitaevskii; Ginzburg-Landau; Vortex rings; finite energy solutions

UR - http://eudml.org/doc/277427

ER -

## Citations in EuDML Documents

top- F. Bethuel, G. Orlandi, D. Smets, Vortex motion and phase-vortex interaction in dissipative Ginzburg-Landau dynamics
- Philippe Gravejat, Decay for travelling waves in the Gross–Pitaevskii equation
- Mihai Mariş, Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity: some results and open problems
- Fabrice Béthuel, Philippe Gravejat, Jean-Claude Saut, Ondes progressives pour l’équation de Gross-Pitaevskii
- Didier Smets, Problèmes d’évolution liés à l’énergie de Ginzburg-Landau
- P. Gérard, The Cauchy problem for the Gross–Pitaevskii equation
- Fabrice Bethuel, Giandomenico Orlandi, Didier Smets, Motion of concentration sets in Ginzburg-Landau equations
- Fabrice Bethuel, Giandomenico Orlandi, Didier Smets, Improved estimates for the Ginzburg-Landau equation : the elliptic case

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