{"title":"Direct linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces","authors":"Shangshuai Li, Da-jun Zhang","doi":"arxiv-2403.06055","DOIUrl":null,"url":null,"abstract":"The paper establishes a direct linearization scheme for the SU(2)\nanti-self-dual Yang-Mills (ASDYM) equation.The scheme starts from a set of\nlinear integral equations with general measures and plane wave factors. After\nintroducing infinite-dimensional matrices as master functions, we are able to\ninvestigate evolution relations and recurrence relations of these functions,\nwhich lead us to the unreduced ASDYM equation. It is then reduced to the ASDYM\nequation in the Euclidean space and two ultrahyperbolic spaces by reductions to\nmeet the reality conditions and gauge conditions, respectively. Special\nsolutions can be obtained by choosing suitable measures.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Exactly Solvable and Integrable Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.06055","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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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