{"title":"生成与一类新的高维列向量环代数相关的高维等谱-非等谱可积分层次结构","authors":"Haifeng Wang, Yufeng Zhang","doi":"10.1134/S0040577924050039","DOIUrl":null,"url":null,"abstract":"<p> We construct a new class of higher-dimensional column-vector loop algebras. Based on it, a method for generating higher-dimensional isospectral–nonisospectral integrable hierarchies is proposed. As an application, we derive a generalized nonisospectral integrable Schrödinger hierarchy that can be reduced to the famous derivative nonlinear Schrödinger equation. By using the higher-dimensional column-vector loop algebras, we obtain an extended isospectral–nonisospectral integrable Schrödinger hierarchy that can be reduced to many classical and new equations, such as the extended nonisospectral derivative nonlinear Schrödinger system, the heat equation, and the Fokker–Planck equation, which has a wide range of applications in stochastic dynamical systems. Furthermore, we deduce a <span>\\(Z_N^\\varepsilon\\)</span> nonisospectral integrable Schrödinger hierarchy, which means that the coupling results are extended to an arbitrary number of components. Additionally, the Hamiltonian structures of these hierarchies are discussed by using the quadratic form trace identity. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 2","pages":"722 - 747"},"PeriodicalIF":1.0000,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generation of higher-dimensional isospectral–nonisospectral integrable hierarchies associated with a new class of higher-dimensional column-vector loop algebras\",\"authors\":\"Haifeng Wang, Yufeng Zhang\",\"doi\":\"10.1134/S0040577924050039\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> We construct a new class of higher-dimensional column-vector loop algebras. Based on it, a method for generating higher-dimensional isospectral–nonisospectral integrable hierarchies is proposed. As an application, we derive a generalized nonisospectral integrable Schrödinger hierarchy that can be reduced to the famous derivative nonlinear Schrödinger equation. By using the higher-dimensional column-vector loop algebras, we obtain an extended isospectral–nonisospectral integrable Schrödinger hierarchy that can be reduced to many classical and new equations, such as the extended nonisospectral derivative nonlinear Schrödinger system, the heat equation, and the Fokker–Planck equation, which has a wide range of applications in stochastic dynamical systems. Furthermore, we deduce a <span>\\\\(Z_N^\\\\varepsilon\\\\)</span> nonisospectral integrable Schrödinger hierarchy, which means that the coupling results are extended to an arbitrary number of components. Additionally, the Hamiltonian structures of these hierarchies are discussed by using the quadratic form trace identity. </p>\",\"PeriodicalId\":797,\"journal\":{\"name\":\"Theoretical and Mathematical Physics\",\"volume\":\"219 2\",\"pages\":\"722 - 747\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-05-24\",\"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/S0040577924050039\",\"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/S0040577924050039","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}
Generation of higher-dimensional isospectral–nonisospectral integrable hierarchies associated with a new class of higher-dimensional column-vector loop algebras
We construct a new class of higher-dimensional column-vector loop algebras. Based on it, a method for generating higher-dimensional isospectral–nonisospectral integrable hierarchies is proposed. As an application, we derive a generalized nonisospectral integrable Schrödinger hierarchy that can be reduced to the famous derivative nonlinear Schrödinger equation. By using the higher-dimensional column-vector loop algebras, we obtain an extended isospectral–nonisospectral integrable Schrödinger hierarchy that can be reduced to many classical and new equations, such as the extended nonisospectral derivative nonlinear Schrödinger system, the heat equation, and the Fokker–Planck equation, which has a wide range of applications in stochastic dynamical systems. Furthermore, we deduce a \(Z_N^\varepsilon\) nonisospectral integrable Schrödinger hierarchy, which means that the coupling results are extended to an arbitrary number of components. Additionally, the Hamiltonian structures of these hierarchies are discussed by using the quadratic form trace identity.
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.