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53-XX Differential geometry
53Zxx Applications to physics

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Variational metrics on $𝐑 \times T M$ and the geometry of nonconservative mechanics

Olga Krupková (1994)

Mathematica Slovaca

Variations on the theme of twistor spaces.

Vaisman, I. (1998)

Balkan Journal of Geometry and its Applications (BJGA)

Vortex rings for the Gross-Pitaevskii equation

Fabrice Bethuel, G. Orlandi, Didier Smets (2004)

Journal of the European Mathematical Society

We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross–Pitaevskii (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 $N = 3$ ).

Currently displaying 1 – 3 of 3