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BÄCKLUND TRANSFORMATIONS FOR NON-COMMUTATIVE ANTI-SELF-DUAL YANG–MILLS EQUATIONS

Published online by Cambridge University Press:  01 February 2009

CLAIRE R. GILSON
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK e-mail: crg@maths.gla.ac.uk
MASASHI HAMANAKA
Affiliation:
Department of Mathematics, University of Nagoya, Nagoya 464-8602, Japan e-mail: hamanaka@math.nagoya-u.ac.jp
JONATHAN J. C. NIMMO
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK e-mail: j.nimmo@maths.gla.ac.uk
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Abstract

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We present Bäcklund transformations for the non-commutative anti-self-dual Yang–Mills equations 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 quasi-determinants and belong to a non-commutative version of the Atiyah–Ward ansatz. In the commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard.

Keywords

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

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