Orbital stability of smooth solitons for the modified Camassa-Holm equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-08-02 DOI:10.1016/j.aim.2024.109870

Ji Li , Yue Liu , Guangming Zhu

{"title":"Orbital stability of smooth solitons for the modified Camassa-Holm equation","authors":"Ji Li , Yue Liu , Guangming Zhu","doi":"10.1016/j.aim.2024.109870","DOIUrl":null,"url":null,"abstract":"<div>The modified Camassa-Holm equation with cubic nonlinearity is completely integrable and is considered a model for the unidirectional propagation of shallow-water waves. The localized smooth-wave solution exists uniquely, up to translation, within a certain range of the linear dispersive parameter. By constructing conserved <math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math> and <math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math> quantities in terms of the momentum variable m, this study demonstrates that the smooth soliton, when regarded as a solution of the initial-value problem for the modified Camassa-Holm equation, is orbitally stable to perturbations in the Sobolev space <math><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup></math>. Furthermore, the global well-posedness of the solution is established for certain initial data in <math><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup></math> with <math><mi>s</mi><mo>≥</mo><mn>3</mn></math>.</div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0001870824003852","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

Abstract

The modified Camassa-Holm equation with cubic nonlinearity is completely integrable and is considered a model for the unidirectional propagation of shallow-water waves. The localized smooth-wave solution exists uniquely, up to translation, within a certain range of the linear dispersive parameter. By constructing conserved $H^{1}$ and $L^{1}$ quantities in terms of the momentum variable m, this study demonstrates that the smooth soliton, when regarded as a solution of the initial-value problem for the modified Camassa-Holm equation, is orbitally stable to perturbations in the Sobolev space $H^{3}$ . Furthermore, the global well-posedness of the solution is established for certain initial data in $H^{s}$ with $s \geq 3$ .

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

修正卡马萨-霍尔姆方程的光滑孤子轨道稳定性

具有立方非线性的修正卡马萨-霍姆方程是完全可积分的，被认为是浅水波单向传播的模型。在线性色散参数的一定范围内，局部平滑波解唯一存在，直至平移。通过构建动量变量 m 的 H1 和 L1 守恒量，本研究证明，将平滑孤子视为修正卡马萨-霍尔姆方程初值问题的解时，它对 Sobolev 空间 H3 中的扰动具有轨道稳定性。此外，对于 s≥3 的 Hs 中的某些初始数据，建立了该解的全局好求解性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

期刊最新文献

Management of Cholesteatoma: Hearing Rehabilitation. Congenital Cholesteatoma. Evaluation of Cholesteatoma. Management of Cholesteatoma: Extension Beyond Middle Ear/Mastoid. Recidivism and Recurrence.