Bäcklund Transformations for Noncommutative Anti-Self-Dual Yang-Mills Equations

Details Bäcklund Transformations for Noncommutative Anti-Self-Dual Yang-Mills Equations Bäcklund Transformations for Noncommutative Anti-Self-Dual Yang-Mills Equations

2007-09-13

arxiv.org/abs/0709.2069v2

Glasgow Mathematical Journal 51A (2009) 83-93

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages; version to appear in Glasgow Mathematical Journal

Scientific paper

10.1017/S0017089508004801

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.

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