Existence and uniqueness of generalized vortices

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Abstract
We investigate properties of the static noninteracting vortices determined by equations which generalize the first order Ginzburg–Landau equations. We prove that for each set of n points in the plane a unique solution exists to the first-order equations, with vortex number n. These n points mark the positions of the n vortices and are the only points at which the Higgs field ‖φ‖ vanishes. Regularity properties of the solution are related to those of an arbitrary non-negative function in the theory.

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