周期函数类中广义Camassa-Holm方程的积分

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI:10.1134/S0040577925040075

B. A. Babajanov, D. O. Atajonov

{"title":"周期函数类中广义Camassa-Holm方程的积分","authors":"B. A. Babajanov, D. O. Atajonov","doi":"10.1134/S0040577925040075","DOIUrl":null,"url":null,"abstract":" We study periodic solutions of the generalized Camassa–Holm equation (CH-\\(\\gamma\\) equation). We show that the generalized CH-\\(\\gamma\\) equation is also an important theoretical model because it is a completely integrable system. We obtain representation for periodic solutions of the generalized CH-\\(\\gamma\\) equation in the framework of the inverse spectral problem for a weighted Sturm–Liouville operator. ","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 1","pages":"624 - 635"},"PeriodicalIF":1.0000,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Integration of the generalized Camassa–Holm equation in the class of periodic functions\",\"authors\":\"B. A. Babajanov, D. O. Atajonov\",\"doi\":\"10.1134/S0040577925040075\",\"DOIUrl\":null,\"url\":null,\"abstract\":\" We study periodic solutions of the generalized Camassa–Holm equation (CH-\\\\(\\\\gamma\\\\) equation). We show that the generalized CH-\\\\(\\\\gamma\\\\) equation is also an important theoretical model because it is a completely integrable system. We obtain representation for periodic solutions of the generalized CH-\\\\(\\\\gamma\\\\) equation in the framework of the inverse spectral problem for a weighted Sturm–Liouville operator. \",\"PeriodicalId\":797,\"journal\":{\"name\":\"Theoretical and Mathematical Physics\",\"volume\":\"223 1\",\"pages\":\"624 - 635\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2025-04-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical and Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0040577925040075\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S0040577925040075","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

研究了广义Camassa-Holm方程（CH- \(\gamma\)方程）的周期解。我们证明了广义CH- \(\gamma\)方程也是一个重要的理论模型，因为它是一个完全可积系统。在加权Sturm-Liouville算子的逆谱问题框架下，得到了广义CH- \(\gamma\)方程周期解的表示形式。

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

Integration of the generalized Camassa–Holm equation in the class of periodic functions

We study periodic solutions of the generalized Camassa–Holm equation (CH-\(\gamma\) equation). We show that the generalized CH-\(\gamma\) equation is also an important theoretical model because it is a completely integrable system. We obtain representation for periodic solutions of the generalized CH-\(\gamma\) equation in the framework of the inverse spectral problem for a weighted Sturm–Liouville operator.

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

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.