Vortex solutions of the Popov equations

Abstract

Popov recently discovered a modified version of the Bogomolny equations for abelian Higgs vortices, and showed they were integrable on a sphere of curvature 1/2. Here we construct a large family of explicit solutions, where the vortex number is an even integer. There are also a few solutions without vortices. The solutions are constructed from rational functions on the sphere.

Version 2, 9 pages. Additional discussion of vortex energies. This version solves equations for vortices, rather than anti-vortices. Vortices are "holomorphic" and have positive first Chern number

References in corpus (1)

• Integrable vortex-type equations on the two-sphere

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