{"title":"Transmission of fast solitons for the NLS with an external potential","authors":"Christopher C. Hogan, Jason Murphy","doi":"10.3934/dcds.2023142","DOIUrl":null,"url":null,"abstract":"We consider the dynamics of a boosted soliton evolving under the cubic NLS with an external potential. We show that for sufficiently large velocities, the soliton is effectively transmitted through the potential. This result extends work of Holmer, Marzuola, and Zworski, who considered the case of a delta potential with no bound states, and work of Datchev and Holmer, who considered the case of a delta potential with a linear bound state.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/dcds.2023142","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the dynamics of a boosted soliton evolving under the cubic NLS with an external potential. We show that for sufficiently large velocities, the soliton is effectively transmitted through the potential. This result extends work of Holmer, Marzuola, and Zworski, who considered the case of a delta potential with no bound states, and work of Datchev and Holmer, who considered the case of a delta potential with a linear bound state.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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