Soliton Solutions of Noncommutative Anti-Self-Dual Yang-Mills Equations

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...

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Published in:arXiv.org 2020-07
Main Authors: Gilson, Claire R, Hamanaka, Masashi, Shan-Chi, Huang, Nimmo, Jonathan J C
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Domain walls
Euclidean geometry
Flux density
Mathematical analysis
Solitary waves
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Hamanaka, Masashi
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description 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.
doi_str_mv 10.48550/arxiv.2004.01718
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subjects Domain walls
Euclidean geometry
Flux density
Mathematical analysis
Solitary waves
title Soliton Solutions of Noncommutative Anti-Self-Dual Yang-Mills Equations
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