Vortex solutions of the Popov equations

TL;DR

This paper constructs explicit vortex solutions to the modified Popov equations on a sphere, revealing integrability and providing a large family of solutions derived from rational functions.

Contribution

It introduces a method to explicitly solve the Popov vortex equations on a sphere using rational functions, expanding the set of known solutions.

Findings

Explicit solutions for vortex number as even integers

Solutions constructed from rational functions on the sphere

Existence of solutions without vortices

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.