The Yang Mills system and cyclic covering of abelian varieties

TL;DR

This paper explores a dynamical system related to the Yang-Mills equations with gauge group SU(2), solving it using genus two hyperelliptic functions and demonstrating its algebraic complete integrability.

Contribution

It introduces a novel solution to the Yang-Mills related system using hyperelliptic functions and establishes its algebraic complete integrability in a generalized framework.

Findings

Solution expressed via genus two hyperelliptic functions

Proved algebraic complete integrability of the system

Connected the system to the theory of algebraic curves

Abstract

In this paper, we consider a dynamical system related to the Yang-Mills system for a field with gauge group SU(2). We solve this system in terms of genus two hyperelliptic functions and we show that it is algebraic completely integrable in the generalized sense.