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arXiv · 2004.01718

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

Claire R. Gilson·Masashi Hamanaka·Shan-Chi Huang·Jonathan J. C. Nimmo
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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.

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Claire R. Gilson, Masashi Hamanaka, Shan-Chi Huang, Jonathan J. C. Nimmo. 2020-04-03. Soliton Solutions of Noncommutative Anti-Self-Dual Yang-Mills Equations. https://doi.org/10.1088/1751-8121%2Faba72e

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