Burgers和Hopf方程的简单解

IF 0.8 3区数学 Q2 MATHEMATICS

Izvestiya Mathematics Pub Date : 2021-01-01 DOI:10.1070/IM9051

V. K. Beloshapka

{"title":"Burgers和Hopf方程的简单解","authors":"V. K. Beloshapka","doi":"10.1070/IM9051","DOIUrl":null,"url":null,"abstract":"We describe all solutions of the Burgers equation of analytic complexity not exceeding . It turns out that all such solutions fall into four families of dimensions not exceeding that are represented by elementary functions. An example of a family of solutions of the Burgers equation of complexity is given. A similar problem is also solved for the Hopf equation. It turns out that all solutions to the Hopf equation of complexity form a two-parameter family of fractional-linear functions which coincides with one of the families of solutions of the Burgers equation.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"343 - 350"},"PeriodicalIF":0.8000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Simple solutions of the Burgers and Hopf equations\",\"authors\":\"V. K. Beloshapka\",\"doi\":\"10.1070/IM9051\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We describe all solutions of the Burgers equation of analytic complexity not exceeding . It turns out that all such solutions fall into four families of dimensions not exceeding that are represented by elementary functions. An example of a family of solutions of the Burgers equation of complexity is given. A similar problem is also solved for the Hopf equation. It turns out that all solutions to the Hopf equation of complexity form a two-parameter family of fractional-linear functions which coincides with one of the families of solutions of the Burgers equation.\",\"PeriodicalId\":54910,\"journal\":{\"name\":\"Izvestiya Mathematics\",\"volume\":\"85 1\",\"pages\":\"343 - 350\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Izvestiya Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1070/IM9051\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1070/IM9051","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们描述了解析复杂度不超过的Burgers方程的所有解。事实证明，所有这些解都属于四个维族，不超过这些维族是由初等函数表示的。给出了复杂的Burgers方程的一类解的例子。对于Hopf方程也解决了一个类似的问题。结果表明，复杂Hopf方程的所有解都形成一个双参数分数线性函数族，这与Burgers方程的一个解族相吻合。

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

Simple solutions of the Burgers and Hopf equations

We describe all solutions of the Burgers equation of analytic complexity not exceeding . It turns out that all such solutions fall into four families of dimensions not exceeding that are represented by elementary functions. An example of a family of solutions of the Burgers equation of complexity is given. A similar problem is also solved for the Hopf equation. It turns out that all solutions to the Hopf equation of complexity form a two-parameter family of fractional-linear functions which coincides with one of the families of solutions of the Burgers equation.

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

Izvestiya Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to: Algebra; Mathematical logic; Number theory; Mathematical analysis; Geometry; Topology; Differential equations.