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

Abstract

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 $\epsilon$ sufficiently small.

References in corpus (2)

• Dynamics Of Ginzburg-Landau And Gross-Pitaevskii Vortices On Manifolds
• Instability of Ginzburg-Landau Vortices on Manifolds