English

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

Exactly Solvable and Integrable Systems 2009-10-22 v2 High Energy Physics - Theory Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.0709.2069,
  title  = {B\"acklund Transformations for Noncommutative Anti-Self-Dual Yang-Mills Equations},
  author = {Claire R. Gilson and Masashi Hamanaka and Jonathan J. C. Nimmo},
  journal= {arXiv preprint arXiv:0709.2069},
  year   = {2009}
}

Comments

10 pages; version to appear in Glasgow Mathematical Journal

R2 v1 2026-06-21T09:17:11.068Z