Abstract
A necessary and sufficient condition is obtained for the existence of multivortex solutions of the Bogomol’nyi system arising in the abelian Higgs theory defined on a rectangular domain and subject to a ’t Hooft type periodic boundary condition. In particular, the number of vortices of a solution is confined by the size of the domain. Such solutions realize the magnetic periodic cell structure in a superconductor predicted by Abrikosov. If the periodic boundary condition is removed, the Bogomol’nyi equations on a bounded domain possess solutions with an arbitrary number of vortices, and these solutions may be used to approximate the unique finite energy solution over the full plane. Moreover, it is shown that, for any given vortex distribution in the plane, the Bogomol’nyi system has a continuous family of gauge-distinct solutions with infinite energy.
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