Existence and uniqueness of solutions to non-Abelian multiple vortex equations on graphs

TL;DR

This paper investigates the conditions under which solutions exist and are unique for a system of non-Abelian multiple vortex equations defined on finite connected graphs, providing a comprehensive mathematical analysis.

Contribution

It establishes a necessary and sufficient condition for the existence and uniqueness of solutions to non-Abelian multiple vortex equations on graphs, advancing mathematical understanding in this area.

Findings

Derived a precise criterion for solution existence

Proved the uniqueness of solutions under certain conditions

Enhanced theoretical understanding of vortex equations on graphs

Abstract

Let $G=(V,E)$ be a connected finite graph. We study a system of non-Abelian multiple vortex equations on $G$. We established a necessary and sufficient condition for the existence and uniqueness of solutions to the non-Abelian multiple vortex equations.