Soliton Solutions of Noncommutative Anti-Self-Dual Yang-Mills Equations
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.
Keywords
Cite
@article{arxiv.2004.01718,
title = {Soliton Solutions of Noncommutative Anti-Self-Dual Yang-Mills Equations},
author = {Claire R. Gilson and Masashi Hamanaka and Shan-Chi Huang and Jonathan J. C. Nimmo},
journal= {arXiv preprint arXiv:2004.01718},
year = {2020}
}
Comments
20 pages; Jonathan Nimmo sadly passed away on 20 June 2017. We owe section 4 to his unpublished note; v2: minor changes, comments added, references added; version to appear in Special Issue of Journal of Physics A on Integrable Physics and its Connections with Special Functions and Combinatorics