Vortex rings for the Gross-Pitaevskii equation (Q1432718)
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scientific article; zbMATH DE number 2075133
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Vortex rings for the Gross-Pitaevskii equation |
scientific article; zbMATH DE number 2075133 |
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Vortex rings for the Gross-Pitaevskii equation (English)
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15 June 2004
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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 \(N=3\)).
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finite energy solutions
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