Direct linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces

2024/03/10 by Shangshuai Li, Da‐jun Zhang, Li, Shangshuai +1
Engineering · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.2403.06055

openalex publication_date 2024/03/10 · openalex created_date 2024/03/13 · openalex updated_date 2026/07/28

Abstract

The paper establishes a direct linearization scheme for the SU(2) anti-self-dual Yang-Mills (ASDYM) equation.The scheme starts from a set of linear integral equations with general measures and plane wave factors. After introducing infinite-dimensional matrices as master functions, we are able to investigate evolution relations and recurrence relations of these functions, which lead us to the unreduced ASDYM equation. It is then reduced to the ASDYM equation in the Euclidean space and two ultrahyperbolic spaces by reductions to meet the reality conditions and gauge conditions, respectively. Special solutions can be obtained by choosing suitable measures.

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