{"title":"Superfield Bäcklund and Darboux transformations of an \\(\\mathcal N=1\\) supersymmetric coupled dispersionless integrable system","authors":"A. Mirza, M. ul Hassan","doi":"10.1134/S0040577924040081","DOIUrl":null,"url":null,"abstract":"<p> We use a superfield Darboux matrix to study Darboux transformations of an <span>\\(\\mathcal N=1\\)</span> supersymmetric coupled dispersionless integrable system. The notion of quasideterminants is used to obtain superfield <span>\\(N\\)</span>-soliton solutions of that system. A superfield Lax representation is used to obtain a superfield Bäcklund transformation via a set of superfield Riccati equations. The Bäcklund and Darboux transformations are further used to compute explicit expressions for superfield soliton solutions of the supersymmetric coupled dispersionless integrable system. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 1","pages":"629 - 637"},"PeriodicalIF":1.0000,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S0040577924040081","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We use a superfield Darboux matrix to study Darboux transformations of an \(\mathcal N=1\) supersymmetric coupled dispersionless integrable system. The notion of quasideterminants is used to obtain superfield \(N\)-soliton solutions of that system. A superfield Lax representation is used to obtain a superfield Bäcklund transformation via a set of superfield Riccati equations. The Bäcklund and Darboux transformations are further used to compute explicit expressions for superfield soliton solutions of the supersymmetric coupled dispersionless integrable system.
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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