Soliton solutions of noncommutative anti-self-dual Yang-Mills equations

Gilson, C. R. , Hamanaka, M., Huang, S.-C. and Nimmo, J. J.C. (2020) Soliton solutions of noncommutative anti-self-dual Yang-Mills equations. Journal of Physics A: Mathematical and Theoretical, 53(40), 404002. (doi: 10.1088/1751-8121/aba72e)

Abstract

We present exact soliton solutions of anti-self-dual Yang-Mills equations for G = GL(N) on noncommutative Euclidean spaces in four-dimension by using the Darboux transformations. Generated solutions are represented by quasideterminants of Wronski matrices in compact forms. We give special one-soliton solutions for G = GL(2) whose energy density can be real-valued. We find that the soliton solutions are the same as the commutative ones and can be interpreted as one-domain walls in four-dimension. Scattering processes of the multi-soliton solutions are also discussed.

• 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., Huang, S.-C., and Nimmo, J. J.C.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Physics A: Mathematical and Theoretical
• Publisher: IOP Publishing
• ISSN: 1751-8113
• ISSN (Online): 1751-8121
• Published Online: 17 July 2020
• Copyright Holders: Copyright © 2020 IOP Publishing Ltd
• First Published: First published in Journal of Physics A: Mathematical and Theoretical 53(40): 404002
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher