{"title":"在 Sturm-Liouville 算子特征值移动的情况下，对带有时变系数的 Korteweg-de Vries 方程进行积分","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":"{\"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}","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}
Integration of the Korteweg–de Vries Equation with Time-Dependent Coefficients in the Case of Moving Eigenvalues of the Sturm–Liouville Operator
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
