{"title":"Quasi-periodic solutions around plane wave of high dimensional nonlinear Schrödinger equation","authors":"Meina Gao , Jianjun Liu , Zejing Liu","doi":"10.1016/j.jde.2025.113229","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, a degenerate KAM theorem with multiple normal frequencies is established under qualitative non-degenerate conditions. As an application, quasi-periodic solutions around plane wave are obtained for high dimensional nonlinear Schrödinger equation with periodic boundary conditions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113229"},"PeriodicalIF":2.3000,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625002372","RegionNum":2,"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
In this paper, a degenerate KAM theorem with multiple normal frequencies is established under qualitative non-degenerate conditions. As an application, quasi-periodic solutions around plane wave are obtained for high dimensional nonlinear Schrödinger equation with periodic boundary conditions.
期刊介绍：
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics
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