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Vortex rings for the Gross-Pitaevskii equation. (English) Zbl 1091.35085
Summary: We provide a mathematical proof of the existence of traveling vortex ring solutions to the Gross-Pitaevskiĭ(GP) equation in dimension \(N\geq 3\). 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 \(N=3\)).

MSC:
35Q56 Ginzburg-Landau equations
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
82D55 Statistical mechanics of superconductors
35C07 Traveling wave solutions
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