Periodic Orbits of Gross Pitaevskii in the Disc with Vortices Following Point Vortex Flow
Abstract
We prove the existence of non-constant time periodic vortex solutions to the Gross-Pitaevskii equations for small but fixed > 0. The vortices of these solutions follow periodic orbits to the point vortex system of ordinary differential equations for all time. The construction uses two approaches-- constrained minimization techniques adapted from GS and topological minimax techniques adapted from LinMinMax, applied to a formulation of the problem within a rotational ansatz.
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