{"title":"实线上的立方 Szegő 方程：哈代类上的显式和解析性","authors":"Patrick Gérard, Alexander Pushnitski","doi":"10.1007/s00220-024-05040-4","DOIUrl":null,"url":null,"abstract":"<p>We establish an explicit formula for the solution of the cubic Szegő equation on the real line. Using this formula, we prove that the evolution flow of this equation can be continuously extended to the whole Hardy class <span>\\(H^2\\)</span> on the real line.\n</p>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Cubic Szegő Equation on the Real Line: Explicit Formula and Well-Posedness on the Hardy Class\",\"authors\":\"Patrick Gérard, Alexander Pushnitski\",\"doi\":\"10.1007/s00220-024-05040-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We establish an explicit formula for the solution of the cubic Szegő equation on the real line. Using this formula, we prove that the evolution flow of this equation can be continuously extended to the whole Hardy class <span>\\\\(H^2\\\\)</span> on the real line.\\n</p>\",\"PeriodicalId\":522,\"journal\":{\"name\":\"Communications in Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s00220-024-05040-4\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s00220-024-05040-4","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
The Cubic Szegő Equation on the Real Line: Explicit Formula and Well-Posedness on the Hardy Class
We establish an explicit formula for the solution of the cubic Szegő equation on the real line. Using this formula, we prove that the evolution flow of this equation can be continuously extended to the whole Hardy class \(H^2\) on the real line.
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The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.
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