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

Nonlinear Sciences – Exactly Solvable and Integrable Systems

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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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