论三个双分量双哈密顿系统的可积分性

IF 2 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-07-19 DOI:10.1088/1751-8121/ad65a1

L. Zang, Qian Zhang, Qingping Liu

{"title":"论三个双分量双哈密顿系统的可积分性","authors":"L. Zang, Qian Zhang, Qingping Liu","doi":"10.1088/1751-8121/ad65a1","DOIUrl":null,"url":null,"abstract":"\n The compatible trios of two-component homogeneous Hamiltonian operators were classified and some bi-Hamiltonian systems were constructed by Lorenzoni, Savoldi, and Vitolo [J. Phys. A: Math. Theor. {\\bf{51}} (2018) 045202]. In this paper, we study three two-component bi-Hamiltonian systems proposed by them. By means of the prolongation structure technique, we construct the missing Lax representations for those systems and confirm their integrability. Furthermore, we explore the possible connections between those systems and the known integrable systems.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the integrability of three two-component bi-Hamiltonian systems\",\"authors\":\"L. Zang, Qian Zhang, Qingping Liu\",\"doi\":\"10.1088/1751-8121/ad65a1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n The compatible trios of two-component homogeneous Hamiltonian operators were classified and some bi-Hamiltonian systems were constructed by Lorenzoni, Savoldi, and Vitolo [J. Phys. A: Math. Theor. {\\\\bf{51}} (2018) 045202]. In this paper, we study three two-component bi-Hamiltonian systems proposed by them. By means of the prolongation structure technique, we construct the missing Lax representations for those systems and confirm their integrability. Furthermore, we explore the possible connections between those systems and the known integrable systems.\",\"PeriodicalId\":16763,\"journal\":{\"name\":\"Journal of Physics A: Mathematical and Theoretical\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2024-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Physics A: Mathematical and Theoretical\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1751-8121/ad65a1\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physics A: Mathematical and Theoretical","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1751-8121/ad65a1","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

Lorenzoni、Savoldi和Vitolo对两分量同质哈密顿算子的兼容三元组进行了分类，并构造了一些双哈密顿系统[J. Phys. A: Math. Theor. {\bf{51}} (2018) 045202]。本文研究了他们提出的三个双分量双哈密顿系统。通过延长结构技术，我们为这些系统构造了缺失的Lax表示，并证实了它们的可整性。此外，我们还探讨了这些系统与已知可积分系统之间可能存在的联系。

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

On the integrability of three two-component bi-Hamiltonian systems

The compatible trios of two-component homogeneous Hamiltonian operators were classified and some bi-Hamiltonian systems were constructed by Lorenzoni, Savoldi, and Vitolo [J. Phys. A: Math. Theor. {\bf{51}} (2018) 045202]. In this paper, we study three two-component bi-Hamiltonian systems proposed by them. By means of the prolongation structure technique, we construct the missing Lax representations for those systems and confirm their integrability. Furthermore, we explore the possible connections between those systems and the known integrable systems.

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 Physics A: Mathematical and Theoretical 物理-物理：数学物理

CiteScore

4.10

自引率

14.30%

发文量

542

审稿时长

1.9 months

期刊介绍： Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.