# Some exact Bradlow vortex solutions

## TL;DR

This paper presents a new class of exact analytical solutions to the Bradlow vortex equation on complex geometries with variable curvature, expanding the understanding of vortex configurations in mathematical physics.

## Contribution

It introduces a two-parameter family of closed-form solutions involving hypergeometric functions for the Bradlow vortex equation on nontrivial geometries.

## Key findings

- Solutions expressed via hypergeometric functions
- Analytic solutions on geometries with non-constant curvature
- Explicit formulas for vortex domain area

## Abstract

We consider the Bradlow equation for vortices which was recently found by Manton and find a two-parameter class of analytic solutions in closed form on nontrivial geometries with non-constant curvature. The general solution to our class of metrics is given by a hypergeometric function and the area of the vortex domain by the Gaussian hypergeometric function.