{"title":"Integration of the Korteweg–de Vries Equation with Time-Dependent Coefficients in the Case of Moving Eigenvalues of the Sturm–Liouville Operator","authors":"U. A. Hoitmetov, T. G. Khasanov","doi":"10.3103/s1066369x2470035x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The inverse scattering method is used to integrate the Korteweg–de Vries equation with time-dependent coefficients. We derive the evolution of the scattering data of the Sturm–Liouville operator whose coefficient is a solution of the Korteweg–de Vries equation with time-dependent coefficients. An algorithm for constructing exact solutions of the Korteweg–de Vries equation with time-dependent coefficients is also proposed; we reduce it to the inverse problem of scattering theory for the Sturm–Liouville operator. Examples illustrating the stated algorithm are given.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"316 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x2470035x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The inverse scattering method is used to integrate the Korteweg–de Vries equation with time-dependent coefficients. We derive the evolution of the scattering data of the Sturm–Liouville operator whose coefficient is a solution of the Korteweg–de Vries equation with time-dependent coefficients. An algorithm for constructing exact solutions of the Korteweg–de Vries equation with time-dependent coefficients is also proposed; we reduce it to the inverse problem of scattering theory for the Sturm–Liouville operator. Examples illustrating the stated algorithm are given.
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