{"title":"Stability of standing waves for a generalized Benney-Roskes system","authors":"Jose R. Quintero","doi":"10.1090/qam/1654","DOIUrl":null,"url":null,"abstract":"We analyze the orbital stability of standing waves for a generalized Benney-Roskes system in spatial dimensions \n\n \n \n N\n =\n 2\n \n N=2\n \n\n, \n\n \n 3\n 3\n \n\n. We establish stability of standing waves under certain conditions by reducing the system to a single nonlinear (nonlocal) Schrödinger equation, using the variational characterization of standing waves and a convexity argument.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quarterly of Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/qam/1654","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We analyze the orbital stability of standing waves for a generalized Benney-Roskes system in spatial dimensions
N
=
2
N=2
,
3
3
. We establish stability of standing waves under certain conditions by reducing the system to a single nonlinear (nonlocal) Schrödinger equation, using the variational characterization of standing waves and a convexity argument.
期刊介绍：
The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume.
This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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