广义Korteweg-de-Vries方程的非色散解通常是多孤子

IF 1.8 1区数学 Q1 MATHEMATICS, APPLIED

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-09-01 DOI:10.1016/j.anihpc.2020.11.010

Xavier Friederich

{"title":"广义Korteweg-de-Vries方程的非色散解通常是多孤子","authors":"Xavier Friederich","doi":"10.1016/j.anihpc.2020.11.010","DOIUrl":null,"url":null,"abstract":"<div><p>We consider solutions of the generalized Korteweg-de Vries equations (gKdV) which are non dispersive in some sense and which remain close to multi-solitons. We show that these solutions are necessarily pure multi-solitons. For the Korteweg-de Vries equation (KdV) and the modified Korteweg-de Vries equation (mKdV) in particular, we obtain a characterization of multi-solitons and multi-breathers in terms of non dispersion.</p></div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2020.11.010","citationCount":"2","resultStr":"{\"title\":\"Non dispersive solutions of the generalized Korteweg-de Vries equations are typically multi-solitons\",\"authors\":\"Xavier Friederich\",\"doi\":\"10.1016/j.anihpc.2020.11.010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider solutions of the generalized Korteweg-de Vries equations (gKdV) which are non dispersive in some sense and which remain close to multi-solitons. We show that these solutions are necessarily pure multi-solitons. For the Korteweg-de Vries equation (KdV) and the modified Korteweg-de Vries equation (mKdV) in particular, we obtain a characterization of multi-solitons and multi-breathers in terms of non dispersion.</p></div>\",\"PeriodicalId\":55514,\"journal\":{\"name\":\"Annales De L Institut Henri Poincare-Analyse Non Lineaire\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2021-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.anihpc.2020.11.010\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales De L Institut Henri Poincare-Analyse Non Lineaire\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0294144920301256\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0294144920301256","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 2

摘要

我们考虑广义Korteweg-de-Vries方程（gKdV）的解，该方程在某种意义上是非色散的，并且仍然接近于多孤子。我们证明了这些解必然是纯的多孤子。特别是对于Korteweg-de-Vries方程（KdV）和修正的Korteweg de Vries方程，我们获得了多孤子和多呼吸子的非色散特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Non dispersive solutions of the generalized Korteweg-de Vries equations are typically multi-solitons

We consider solutions of the generalized Korteweg-de Vries equations (gKdV) which are non dispersive in some sense and which remain close to multi-solitons. We show that these solutions are necessarily pure multi-solitons. For the Korteweg-de Vries equation (KdV) and the modified Korteweg-de Vries equation (mKdV) in particular, we obtain a characterization of multi-solitons and multi-breathers in terms of non dispersion.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annales De L Institut Henri Poincare-Analyse Non Lineaire 数学-应用数学

CiteScore

4.10

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.