弗拉索夫-泊松系统的游波

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-02-13 DOI:10.1016/j.jde.2025.02.021

Masahiro Suzuki , Masahiro Takayama , Katherine Zhiyuan Zhang

{"title":"弗拉索夫-泊松系统的游波","authors":"Masahiro Suzuki , Masahiro Takayama , Katherine Zhiyuan Zhang","doi":"10.1016/j.jde.2025.02.021","DOIUrl":null,"url":null,"abstract":"<div><div>We consider the Vlasov–Poisson system describing a two-species plasma with spatial dimension 1 and the velocity variable in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We find the necessary and sufficient conditions for the existence of solitary waves, shock waves, and wave trains of the system, respectively. To this end, we need to investigate solutions that are not BGK waves. Furthermore, we classify completely in all possible cases whether or not the traveling wave is unique. The uniqueness varies according to each traveling wave when we exclude the variant caused by translation. For the solitary wave, there are both cases that it is unique and nonunique. The shock wave is always unique. No wave train is unique.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"428 ","pages":"Pages 230-290"},"PeriodicalIF":2.4000,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Traveling waves of the Vlasov–Poisson system\",\"authors\":\"Masahiro Suzuki , Masahiro Takayama , Katherine Zhiyuan Zhang\",\"doi\":\"10.1016/j.jde.2025.02.021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We consider the Vlasov–Poisson system describing a two-species plasma with spatial dimension 1 and the velocity variable in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We find the necessary and sufficient conditions for the existence of solitary waves, shock waves, and wave trains of the system, respectively. To this end, we need to investigate solutions that are not BGK waves. Furthermore, we classify completely in all possible cases whether or not the traveling wave is unique. The uniqueness varies according to each traveling wave when we exclude the variant caused by translation. For the solitary wave, there are both cases that it is unique and nonunique. The shock wave is always unique. No wave train is unique.</div></div>\",\"PeriodicalId\":15623,\"journal\":{\"name\":\"Journal of Differential Equations\",\"volume\":\"428 \",\"pages\":\"Pages 230-290\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2025-02-13\",\"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/S0022039625001408\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625001408","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

摘要

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

Traveling waves of the Vlasov–Poisson system

We consider the Vlasov–Poisson system describing a two-species plasma with spatial dimension 1 and the velocity variable in

R^{n}

. We find the necessary and sufficient conditions for the existence of solitary waves, shock waves, and wave trains of the system, respectively. To this end, we need to investigate solutions that are not BGK waves. Furthermore, we classify completely in all possible cases whether or not the traveling wave is unique. The uniqueness varies according to each traveling wave when we exclude the variant caused by translation. For the solitary wave, there are both cases that it is unique and nonunique. The shock wave is always unique. No wave train is unique.

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

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

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