The Generalized Point-Vortex Problem and Rotating Solutions to the Gross-Pitaevskii Equation on Surfaces of Revolution

We study the generalized point-vortex problem and the Gross-Pitaevskii equation on surfaces of revolution. We find rotating periodic solutions to the generalized point-vortex problem, which have two two rings of $n$ equally spaced vortices with degrees $\pm 1$. In particular we prove the existence of such solutions when the surface is longitudinally symmetric. Then we seek a rotating solution to the Gross-Pitaevskii equation having vortices that follow those of the point-vortex flow for $\varepsilon$ sufficiently small.

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