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arXiv · 0709.2069

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

Claire R. Gilson·Masashi Hamanaka·Jonathan J. C. Nimmo
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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.

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Claire R. Gilson, Masashi Hamanaka, Jonathan J. C. Nimmo. 2008-06-12. Bäcklund Transformations for Noncommutative Anti-Self-Dual Yang-Mills Equations. https://doi.org/10.1017/s0017089508004801

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