Backlund transformations and the Atiyah-Ward ansatz for non-commutative anti-self-dual Yang-Mills equations

Gilson, C. R. , Hamanaka, M. and Nimmo, J. J. C. (2009) Backlund transformations and the Atiyah-Ward ansatz for non-commutative anti-self-dual Yang-Mills equations. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 465(2108), pp. 2613-2632. (doi: 10.1098/rspa.2008.0515)

Abstract

We present Backlund transformations for the non-commutative 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 quasi-determinants. We also explain the origins of all the ingredients of the Backlund transformations within the framework of non-commutative twistor theory. In particular, we show that the generated solutions belong to a non-commutative version of the Atiyah-Ward ansatz.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Gilson, Dr Claire and Nimmo, Dr Jonathan
• Authors: Gilson, C. R., Hamanaka, M., and Nimmo, J. J. C.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences
• ISSN: 1364-5021
• ISSN (Online): 1471-2946