{"title":"非线性偏微分方程的拟周期解","authors":"Wei-Min Wang","doi":"10.1142/9789811208379_0003","DOIUrl":null,"url":null,"abstract":"We present recent developments in the theory of quasi-periodic solutions to nonlinear PDEs, such as the nonlinear Schrodinger and the nonlinear Klein-Gordon equations. These solutions hold in arbitrary dimensions, and the quasi-periodicity can be either in time or space. The method hinges on multi-scale analysis, harmonic analysis and algebraic analysis.","PeriodicalId":292296,"journal":{"name":"Series in Contemporary Applied Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Quasi-Periodic Solutions to Nonlinear PDEs\",\"authors\":\"Wei-Min Wang\",\"doi\":\"10.1142/9789811208379_0003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present recent developments in the theory of quasi-periodic solutions to nonlinear PDEs, such as the nonlinear Schrodinger and the nonlinear Klein-Gordon equations. These solutions hold in arbitrary dimensions, and the quasi-periodicity can be either in time or space. The method hinges on multi-scale analysis, harmonic analysis and algebraic analysis.\",\"PeriodicalId\":292296,\"journal\":{\"name\":\"Series in Contemporary Applied Mathematics\",\"volume\":\"13 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Series in Contemporary Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/9789811208379_0003\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Series in Contemporary Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/9789811208379_0003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We present recent developments in the theory of quasi-periodic solutions to nonlinear PDEs, such as the nonlinear Schrodinger and the nonlinear Klein-Gordon equations. These solutions hold in arbitrary dimensions, and the quasi-periodicity can be either in time or space. The method hinges on multi-scale analysis, harmonic analysis and algebraic analysis.
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