{"title":"Darboux transformations in the inverse scattering problem","authors":"Mukhtar Shamil'evich Badakhov, A. Shabat","doi":"10.13108/2016-8-4-42","DOIUrl":null,"url":null,"abstract":"As it is known, Darboux transformations play a key role in applications in ISP. In the paper we expose the theory of such transformations for the Schrödinger equations with compactly supported potential, which are not necessarily smooth. We study a new class of transformations connected with the zeroes of the reflection coefficient located at conjugated points in the complex plane.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"47 1","pages":"42-51"},"PeriodicalIF":0.5000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ufa Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13108/2016-8-4-42","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: 3
Abstract
As it is known, Darboux transformations play a key role in applications in ISP. In the paper we expose the theory of such transformations for the Schrödinger equations with compactly supported potential, which are not necessarily smooth. We study a new class of transformations connected with the zeroes of the reflection coefficient located at conjugated points in the complex plane.
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