Integrable Abelian Vortex-like solitons

TL;DR

This paper identifies integrable cases of modified Ginzburg-Landau models that admit vortex-like solitons, providing explicit solutions via Painlevé transcendents and interpreting them as Abelian-Higgs vortices on curved surfaces.

Contribution

It determines all Painlevé-integrable cases of the Bogomolny equations for a modified Ginzburg-Landau functional, offering explicit solutions and physical interpretations.

Findings

Explicit solutions in terms of third Painlevé transcendents

Vortex solutions on surfaces with non-constant curvature

Calculation of vortex number and strength

Abstract

We propose a modified version of the Ginzburg-Landau energy functional admitting static solitons and determine all the Painlev\'e-integrable cases of its Bogomolny equations of a given class of models. Explicit solutions are determined in terms of the third Painlev\'e transcendents, allowing us to calculate physical quantities such as the vortex number and the vortex strength. These solutions can be interpreted as the usual Abelian-Higgs vortices on surfaces of non-constant curvature with conical singularity.