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

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.

💡 Research Summary

The paper addresses the construction of Bäcklund transformations for the non‑commutative anti‑self‑dual Yang‑Mills (ASDYM) equations with gauge group (G = GL(2)). After a concise introduction to non‑commutative geometry and its relevance to integrable field theories, the authors formulate the ASDYM equations on a space where coordinates satisfy (