{"title":"关于一维本尼-罗斯克思系统驻波的好拟性和稳定性分析","authors":"Jose Raul Quintero Henao","doi":"10.5556/j.tkjm.56.2025.5268","DOIUrl":null,"url":null,"abstract":"In this paper, we revisit the well-posedness for the Benney-Roskes system (also known as Zakharov-Rubenchik systems) for N = 1, 2, 3, and establish the nonlinear orbital stability of ground state standing waves in the case N = 1, by using the variational approach induced by the Hamiltonian structure and the Liapunov method.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the well-posedness and stability analysis of standing waves for a 1D-Benney-Roskes system\",\"authors\":\"Jose Raul Quintero Henao\",\"doi\":\"10.5556/j.tkjm.56.2025.5268\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we revisit the well-posedness for the Benney-Roskes system (also known as Zakharov-Rubenchik systems) for N = 1, 2, 3, and establish the nonlinear orbital stability of ground state standing waves in the case N = 1, by using the variational approach induced by the Hamiltonian structure and the Liapunov method.\",\"PeriodicalId\":45776,\"journal\":{\"name\":\"Tamkang Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-07-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tamkang Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5556/j.tkjm.56.2025.5268\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tamkang Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5556/j.tkjm.56.2025.5268","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
在本文中，我们重新探讨了 N = 1、2、3 的 Benney-Roskes 系统（也称为 Zakharov-Rubenchik 系统）的好求解性，并利用哈密顿结构和 Liapunov 方法诱导的变分法，建立了 N = 1 情况下基态驻波的非线性轨道稳定性。
On the well-posedness and stability analysis of standing waves for a 1D-Benney-Roskes system
In this paper, we revisit the well-posedness for the Benney-Roskes system (also known as Zakharov-Rubenchik systems) for N = 1, 2, 3, and establish the nonlinear orbital stability of ground state standing waves in the case N = 1, by using the variational approach induced by the Hamiltonian structure and the Liapunov method.
期刊介绍：
To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
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