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.

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 We owe section 4 to his unpublished note; v2: minor changes, comments added, references added; version to appear in Special Issue of Journal of Physics A on Integrable Physics and its Connections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

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Cited by in corpus (5)

• New Soliton Solutions of Anti-Self-Dual Yang-Mills equations
• Multi-Soliton Dynamics of Anti-Self-Dual Gauge Fields
• Solitons in Open N=2 String Theory
• Darboux Transformation for the Hirota equation
• Soliton Resonances in Four Dimensional Wess-Zumino-Witten Model