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Bianchi permutability for the anti-self-dual Yang-Mills equations

Benincasa, G; Halburd, R; (2016) Bianchi permutability for the anti-self-dual Yang-Mills equations. Studies in Applied Mathematics , 137 (1) pp. 110-122. 10.1111/sapm.12118. Green open access

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Abstract

The anti-self-dual Yang-Mills equations are known to have reductions to many integrable differential equations. A general Bäcklund transformation (BT) for the anti-self-dual Yang-Mills (ASDYM) equations generated by a Darboux matrix with an affine dependence on the spectral parameter is obtained, together with its Bianchi permutability equation. We give examples in which we obtain BTs of symmetry reductions of the ASDYM equations by reducing this ASDYM BT. Some discrete integrable systems are obtained directly from reductions of the ASDYM Bianchi system.

Type: Article
Title: Bianchi permutability for the anti-self-dual Yang-Mills equations
Open access status: An open access version is available from UCL Discovery
DOI: 10.1111/sapm.12118
Publisher version: http://dx.doi.org/10.1111/sapm.12118
Language: English
Additional information: This is the peer reviewed version of the following article: Benincasa, G; Halburd, R; (2016) Bianchi permutability for the anti-self-dual Yang-Mills equations. Studies in Applied Mathematics, which has been published in final form at: http://dx.doi.org/10.1111/sapm.12118. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1477228
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