# Time dependent non-Abelian waves and their stochastic regimes for gauge fields coupled to external sources

## TL;DR

This paper investigates exact solutions of SU(2) Yang-Mills and Yang-Mill-Higgs equations with external sources, revealing stochastic behavior in the Higgs case through analytical and numerical methods.

## Contribution

It provides explicit solutions for gauge fields with external sources and demonstrates stochastic regimes in the Higgs case, combining analytical and numerical analysis.

## Key findings

- Confirmed analytical solutions with numerical simulations for YM.
- Numerical results show stochastic behavior in YMH fields.
- Identified time-dependent non-Abelian wave regimes.

## Abstract

In this paper we explore explicit exact solutions of the $SU(2)$ Yang-Mills (YM) and Yang-Mill-Higgs (YMH) equations with homogeneous and inhomogeneous external sources. Whereas in the case of YM we have confirmed our analytical findings with the numerical simulations, the numerical corroborations in the YMH case yielded the stochastic character of motion for the ensuing fields.