Classical solutions for Yang-Mills-Chern-Simons field coupled to an external source

TL;DR

This paper presents a broad class of exact solutions to Yang-Mills-Chern-Simons theory with external sources, including solitons, waves, and singular solutions, expressed via elliptic functions, revealing their existence over nonzero backgrounds.

Contribution

It introduces a comprehensive set of explicit solutions to the coupled Yang-Mills-Chern-Simons equations using elliptic functions, expanding understanding of their solution space.

Findings

Solutions include localized solitons, trigonometric solutions, and cnoidal waves.

Solutions exist over nonzero backgrounds.

Solutions are expressed in terms of Jacobi elliptic functions.

Abstract

We find wide class of exact solutions of Yang-Mills-Chern-Simons theory coupled to an external source, in terms of doubly periodic Jacobi elliptic functions. The obtained solutions include localized solitons, trigonometric solutions, pure cnoidal waves, and singular solutions in certain parameter range. Furthermore, it is observed that these solutions exist over a nonzero background.