B\"acklund Transformations for Noncommutative Anti-Self-Dual Yang-Mills Equations

TL;DR

This paper develops Backlund transformations for noncommutative anti-self-dual Yang-Mills equations, enabling the generation of exact solutions expressed via quasideterminants, extending classical integrable system methods to noncommutative geometry.

Contribution

It introduces a novel Backlund transformation framework for noncommutative anti-self-dual Yang-Mills equations and constructs solutions using quasideterminants, bridging classical and noncommutative integrable systems.

Findings

Generated exact solutions from simple seed solutions.

Solutions expressed in terms of quasideterminants.

Results reduce to known solutions in the commutative limit.

Abstract

We present Backlund transformations for the noncommutative anti-self-dual Yang-Mills equation where the gauge group is G=GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasideterminants and belong to a noncommutative version of the Atiyah-Ward ansatz. In commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard.