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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,
MASASHI HAMANAKA and
JONATHAN J. C. NIMMO
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

35Q5846L5570S15

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue A , February 2009, pp. 83 - 93
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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