{"title":"Inverse scattering problems for the Dirac operator on the line with partial knowledge of the potential","authors":"Ying Yang, Haiyan Jin, Guangsheng Wei","doi":"10.1007/s13324-025-01029-x","DOIUrl":null,"url":null,"abstract":"<div><p>The inverse scattering problem for the Dirac equation on the real line are considered. It is shown that the potential on the real line is uniquely determined in terms of the mixed scattering data which consists of the knowledge of the potential on the right (left) half line of the real axis and the reflection coefficient from the right (left). In particular, neither the bound states or the bound state norming constants are needed. The method is based on a factorization of a scattering matrix.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-025-01029-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The inverse scattering problem for the Dirac equation on the real line are considered. It is shown that the potential on the real line is uniquely determined in terms of the mixed scattering data which consists of the knowledge of the potential on the right (left) half line of the real axis and the reflection coefficient from the right (left). In particular, neither the bound states or the bound state norming constants are needed. The method is based on a factorization of a scattering matrix.
期刊介绍:
Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.