Existence and uniqueness of solutions to Bogomol'nyi-Prased-Sommerfeld equations on graphs

Abstract

Let $G=(V,E)$ be a connected finite graph. We investigate two Bogomol'nyi-Prased-Sommerfeld equations on $G$. We establish necessary and sufficient conditions for the existence and uniqueness of solutions to the two BPS equations.

arXiv comment17 pages