{"title":"Painlevé analysis of the Sasa–Satsuma equation","authors":"","doi":"10.1016/j.physleta.2024.129900","DOIUrl":null,"url":null,"abstract":"<div><p>The Sasa-Satsuma equation is considered. The Painlevé test for partial differential equations with application of the Kruskal variable is used to investigate the necessary condition of integrability of the equation. It is shown that the equation does not pass the Painlevé test in the general case. However, there exist constraints on parameters of the equation, when all Fuchs indices are integers. In these cases the Laurent series expansions of the solution exit and, consequently, there exist analytical solutions of this partial differential equation. We confirm that there are two integrable cases, at which the Sasa–Satsuma equation passes the Painlevé test. We also obtain that there is another set of parameter values at which the equation can be an integrable.</p></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics Letters A","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0375960124005942","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The Sasa-Satsuma equation is considered. The Painlevé test for partial differential equations with application of the Kruskal variable is used to investigate the necessary condition of integrability of the equation. It is shown that the equation does not pass the Painlevé test in the general case. However, there exist constraints on parameters of the equation, when all Fuchs indices are integers. In these cases the Laurent series expansions of the solution exit and, consequently, there exist analytical solutions of this partial differential equation. We confirm that there are two integrable cases, at which the Sasa–Satsuma equation passes the Painlevé test. We also obtain that there is another set of parameter values at which the equation can be an integrable.
期刊介绍：
Physics Letters A offers an exciting publication outlet for novel and frontier physics. It encourages the submission of new research on: condensed matter physics, theoretical physics, nonlinear science, statistical physics, mathematical and computational physics, general and cross-disciplinary physics (including foundations), atomic, molecular and cluster physics, plasma and fluid physics, optical physics, biological physics and nanoscience. No articles on High Energy and Nuclear Physics are published in Physics Letters A. The journal''s high standard and wide dissemination ensures a broad readership amongst the physics community. Rapid publication times and flexible length restrictions give Physics Letters A the edge over other journals in the field.
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