{"title":"半离散可积分层次结构的二元巴格曼对称性约束和积分几何解","authors":"Yaxin Guan, Xinyue Li, Qiulan Zhao","doi":"10.1134/S0040577924110084","DOIUrl":null,"url":null,"abstract":"<p> We present the binary Bargmann symmetry constraint and algebro-geometric solutions for a semidiscrete integrable hierarchy with a bi-Hamiltonian structure. First, we derive a hierarchy associated with a discrete spectral problem by applying the zero-curvature equation and study its bi-Hamiltonian structure. Then, resorting to the binary Bargmann symmetry constraint for the potentials and eigenfunctions, we decompose the hierarchy into an integrable symplectic map and finite-dimensional integrable Hamiltonian systems. Moreover, with the help of the characteristic polynomial of the Lax matrix, we propose a trigonal curve encompassing two infinite points. On this trigonal curve, we introduce a stationary Baker–Akhiezer function and a meromorphic function, and analyze their asymptotic properties and divisors. Based on these preparations, we obtain algebro-geometric solutions for the hierarchy in terms of the Riemann theta function. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1901 - 1928"},"PeriodicalIF":1.0000,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Binary Bargmann symmetry constraint and algebro-geometric solutions of a semidiscrete integrable hierarchy\",\"authors\":\"Yaxin Guan, Xinyue Li, Qiulan Zhao\",\"doi\":\"10.1134/S0040577924110084\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> We present the binary Bargmann symmetry constraint and algebro-geometric solutions for a semidiscrete integrable hierarchy with a bi-Hamiltonian structure. First, we derive a hierarchy associated with a discrete spectral problem by applying the zero-curvature equation and study its bi-Hamiltonian structure. Then, resorting to the binary Bargmann symmetry constraint for the potentials and eigenfunctions, we decompose the hierarchy into an integrable symplectic map and finite-dimensional integrable Hamiltonian systems. Moreover, with the help of the characteristic polynomial of the Lax matrix, we propose a trigonal curve encompassing two infinite points. On this trigonal curve, we introduce a stationary Baker–Akhiezer function and a meromorphic function, and analyze their asymptotic properties and divisors. Based on these preparations, we obtain algebro-geometric solutions for the hierarchy in terms of the Riemann theta function. </p>\",\"PeriodicalId\":797,\"journal\":{\"name\":\"Theoretical and Mathematical Physics\",\"volume\":\"221 2\",\"pages\":\"1901 - 1928\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-11-26\",\"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/S0040577924110084\",\"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/S0040577924110084","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}
Binary Bargmann symmetry constraint and algebro-geometric solutions of a semidiscrete integrable hierarchy
We present the binary Bargmann symmetry constraint and algebro-geometric solutions for a semidiscrete integrable hierarchy with a bi-Hamiltonian structure. First, we derive a hierarchy associated with a discrete spectral problem by applying the zero-curvature equation and study its bi-Hamiltonian structure. Then, resorting to the binary Bargmann symmetry constraint for the potentials and eigenfunctions, we decompose the hierarchy into an integrable symplectic map and finite-dimensional integrable Hamiltonian systems. Moreover, with the help of the characteristic polynomial of the Lax matrix, we propose a trigonal curve encompassing two infinite points. On this trigonal curve, we introduce a stationary Baker–Akhiezer function and a meromorphic function, and analyze their asymptotic properties and divisors. Based on these preparations, we obtain algebro-geometric solutions for the hierarchy in terms of the Riemann theta function.
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.