{"title":"On the properties of solutions of a system of two nonlinear differential equations associated with the Josephson model","authors":"V. V. Tsegelnik","doi":"10.1134/s0040577924040020","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We investigate the analytic properties of solutions of a system of two first-order nonlinear differential equations with an arbitrary parameter <span>\\(l\\)</span> associated with an overdamped Josephson model. We reduce this system to a system of differential equations that is equivalent to the fifth Painlevé equation with the sets of parameters </p><span>$$\\biggl(\\frac{(1-l)^2}{8}, -\\frac{(1-l)^2}{8},0,-2\\biggr), \\; \\biggl(\\frac{l^2}{8}, -\\frac{l^2}{8},0,-2\\biggr).$$</span><p> We show that the solution of the third Painlevé equation with the parameters <span>\\((-2l, 2l-2,1,-1)\\)</span> can be represented as the ratio of two linear fractional transformations of the solutions of the fifth Painlevé equation (with the parameters in the above sequence) connected by a Bäcklund transformation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"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://doi.org/10.1134/s0040577924040020","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 investigate the analytic properties of solutions of a system of two first-order nonlinear differential equations with an arbitrary parameter \(l\) associated with an overdamped Josephson model. We reduce this system to a system of differential equations that is equivalent to the fifth Painlevé equation with the sets of parameters
We show that the solution of the third Painlevé equation with the parameters \((-2l, 2l-2,1,-1)\) can be represented as the ratio of two linear fractional transformations of the solutions of the fifth Painlevé equation (with the parameters in the above sequence) connected by a Bäcklund transformation.
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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