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

Da-jun Zhang; Shangshuai Li

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

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arxiv 2403.06055 v1 pith:HL6PIUPT submitted 2024-03-10 nlin.SI

Shangshuai Li , Da-jun Zhang This is my paper · ORCID

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keywords equationasdymanti-self-dualconditionsdirectfunctionslinearizationmeasures

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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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