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