{"title":"波动方程的一维逆散射问题","authors":"N. Grinberg","doi":"10.1070/SM1991V070N02ABEH001386","DOIUrl":null,"url":null,"abstract":"A constructive method is given for solving the inverse scattering problem for the wave equation on the line and half-line. The slowness function is assumed to have a derivative everywhere except at a finite number of points, and both it and its derivative are assumed to be functions of bounded variation. In addition, the slowness n(x) is required to tend to 1 sufficiently rapidly as x→∞. In this case the slowness function can be reconstructed from the reflection coefficient.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"37 3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"THE ONE-DIMENSIONAL INVERSE SCATTERING PROBLEM FOR THE WAVE EQUATION\",\"authors\":\"N. Grinberg\",\"doi\":\"10.1070/SM1991V070N02ABEH001386\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A constructive method is given for solving the inverse scattering problem for the wave equation on the line and half-line. The slowness function is assumed to have a derivative everywhere except at a finite number of points, and both it and its derivative are assumed to be functions of bounded variation. In addition, the slowness n(x) is required to tend to 1 sufficiently rapidly as x→∞. In this case the slowness function can be reconstructed from the reflection coefficient.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"37 3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1991V070N02ABEH001386\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1991V070N02ABEH001386","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
THE ONE-DIMENSIONAL INVERSE SCATTERING PROBLEM FOR THE WAVE EQUATION
A constructive method is given for solving the inverse scattering problem for the wave equation on the line and half-line. The slowness function is assumed to have a derivative everywhere except at a finite number of points, and both it and its derivative are assumed to be functions of bounded variation. In addition, the slowness n(x) is required to tend to 1 sufficiently rapidly as x→∞. In this case the slowness function can be reconstructed from the reflection coefficient.
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