Bäcklund transformations for noncommutative anti-self-dual Yang-Mills equations

Gilson, C.R., Hamanaka, M. and Nimmo, J.J.C. (2009) Bäcklund transformations for noncommutative anti-self-dual Yang-Mills equations. Glasgow Mathematical Journal, 51(A), pp. 83-93. (doi: 10.1017/S0017089508004801)

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Publisher's URL: http://dx.doi.org/10.1017/S0017089508004801


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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Gilson, Dr Claire and Nimmo, Dr Jonathan
Authors: Gilson, C.R., Hamanaka, M., and Nimmo, J.J.C.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Glasgow Mathematical Journal
Journal Abbr.:Glasg. math. j.
Publisher:Cambridge University Press
ISSN (Online):1469-509X
Published Online:17 February 2009
Copyright Holders:Copyright © 2009 Cambridge University Press
First Published:First published in Glasgow Mathematical Journal 51(A):83-93
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.

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