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AKNS方程族的一类扩展可积模型

物理学报 2002年第5期51卷 951-954页

作者：郭福奎张玉峰山东科技大学应用数学系泰安271019 大连理工大学应用数学系大连116024

首先构造了loop代数A～2 的一个新的子代数 ,设计了一个等谱问题 .应用屠格式求出了著名的AKNS方程族的一类扩展可积模型 ,即可积耦合 .然后将这种求可积耦合的方法一般化 ,可用于一大类方程族 ,如KN族、GJ族、WKI族等谱系的可积耦合 .... 详细信息

首先构造了loop代数A～2 的一个新的子代数 ,设计了一个等谱问题 .应用屠格式求出了著名的AKNS方程族的一类扩展可积模型 ,即可积耦合 .然后将这种求可积耦合的方法一般化 ,可用于一大类方程族 ,如KN族、GJ族、WKI族等谱系的可积耦合 .提出的方法具有普遍应用价值 .最后作为AKNS方程族的特例。

关键词：扩展可积模型可积耦合 loop代数 AKNS方程族环代数孤立子

Fermion Representation of Quantum Toroidal Algebra

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Communications in Theoretical Physics 2014年第4期61卷 403-408页

作者：蔡立强王丽芳吴可杨洁 School of Mathematical Sciences Capital Normal University Department of Mathematics Jilin University

We construct a fermion analogue of the Fock representation of quantum toroidal algebra and construct the fermion representation of quantum toroidal algebra on the K-theory of Hilbert scheme.

关键词：环代数费米子子表示量子环型希尔伯特 K理论

Two Kinds of New Lie Algebras for Producing Integrable Couplings

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Communications in Theoretical Physics 2006年第2X期46卷 203-208页

作者： YAN Qing-You QI Jian-Xun School of Business Administration North China Electric Power University Beijing 102206 China

Two types of Lie algebras are constructed, which are directly used to deduce the two resulting integrable coupling systems with multi-component potential functions. Many other integrable couplings of the known integra... 详细信息

关键词： KN层可积耦合李代数环代数

Generalized Toda Mechanics Associated with Loop Algebra L（Br）

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Communications in Theoretical Physics 2005年第3期43卷 407-412页

作者： YANGZhan-Ying ZHAOLiu SHIKang-Jie DepartmentofPhysics NorthwestUniversityXi＇an710069China DepartmentofPhysics NankaiUniversityTianjin300071China DepartmentofPhysics NorthwestUniversityXi＇an710069China

A class of generalization of Toda mechanics with long range interactions is constructed in this paper. These systems are associated with the loop algebras E(Br) in the sense that their Lax matrices can be realized in terms of the c=0 representations of the affine Lie algebras B(1). We adopt a pair of ordered integers (m, n) to describe the Toda mechanics system when we present the equations of motion and the Hamiltonian structure. We also extract the classical r matrix which satisfy the classical Yang-Baxter relation. Such generalizations will become systems with noncommutative variables in the quantum case.

关键词： r矩阵泊松换位 Toda多体力学系统环代数

Multi-component Levi Hierarchy and Its Multi-component Integrable Coupling System

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Communications in Theoretical Physics 2005年第6X期44卷 990-996页

作者： XIA Tie-Cheng YOU Fu-Cai ZHAO Wen-Ying Department of Mathematics Shanghai University Shanghai 200444 China Department of Mathematics Bohai University Jinzhou 121000 China

A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multicomponent integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then by making use of the Tu scheme the well-known multi-component Levi hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra X is presented, based on the FM, the multi-component integrable coupling system of the multi-component Levi hierarchy is worked out. The method in this paper can be applied to other nonlinear evolution equation hierarchies.

关键词：多分量Levi层多分量可积偶合系统环代数环论

Generalized Multi-component TC Hierarchy and Its Multi-component Integrable Coupling System

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Communications in Theoretical Physics 2005年第5X期44卷 793-798页

作者： XIA Tie-Cheng YOU Fu-Cai Department of Mathematics Shanghai University Shanghai 200444 China

A new 3M-dimensional Lie algebra X is constructed firstly. Then, the corresponding loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra *** follows that a generalscheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then well-known multi-component TC hierarchy is obtained. Finally,an expanding loop algebra FM of the loop algebra X is presented. Based on the FM, the multi-component integrable coupling system of the generalized multi-component TC hierarchy has been worked out. The method in this paper can be applied to other nonlinear evolution equations hierarchies. It is easy to find that we can construct any finite-dimensional Lie algebra by this approach.

关键词： Lie代数可积分耦合函数环代数 TC层次

A Complex Higher-Dimensional Lie Algebra with Real and Imaginary Structure Constants as Well as Its Decomposition

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Communications in Theoretical Physics 2008年第11期50卷 1021-1026页

作者： ZHANG Yu-Feng Mathematical School Liaoning Normal University Dalian 116029 China

A new Lie algebra G of the Lie algebra sl(2) is constructed with complex entries whose structure constantsare real and imaginary numbers.A loop algebra G corresponding to the Lie algebra G is constructed,for which itis devoted to generating a soliton hierarchy of evolution equations under the framework of generalized zero curvatureequation which is derived from the compatibility of the isospectral problems expressed by Hirota ***,wedecompose the Lie algebra G to obtain the subalgebras G_1 and G_*** the G_2 and its one type of loop algebra (?)_2,aLiouville integrable soliton hierarchy is obtained,furthermore,we obtain its bi-Hamiltonian structure by employing thequadratic-form identity.

关键词：复合李代数结构常数环代数哈密尔顿结构

A Multi-component Matrix Loop Algebra and Its Application

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Communications in Theoretical Physics 2005年第6X期44卷 997-1001页

作者： DONG Huan-He ZHANG Ning Information School Shandong University of Science and Technology Qingdao 266510 China

A set of multi-component matrix Lie algebra is constructed. It follows that a type of new loop algebra AM-1 is presented. An isospectral problem is established. Integrable multi-component hierarchy is obtained by Tu pattern, which possesses tri-Hamiltonian structures. Furthermore, it can be reduced to the well-known AKNS hierarchy and BPT hierarchy. Therefore, the major result of this paper can be regarded as a unified expression integrable model of the AKNS hierarchy and the BPT hierarchy.

关键词： Liouville可积三次Hamiltonian结构环代数环论多分量矩阵

Multi-component C-KdV Hierarchy of Soliton Equations and Its Multi-component Integrable Coupling System

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Communications in Theoretical Physics 2004年第4X期42卷 494-496页

作者： XIATie-Cheng YUFa-Jun CHENDeng-Yuan DepartmentofMathematics BohaiUniversityJinzhou121000China DepartmentofMathematics ShanghaiUniversityShanghai200436China

A new simple loop algebra G M is constructed, which is devoted to establishing an isospectral problem. By making use of Tu scheme, the multi-component C-KdV hierarchy is obtained. Further, an expanding loop algebra FM of the loop algebra G M is presented. Based on FM , the multi-component integrable coupling system of the multi-component C-KdV hierarchy is worked out. The method can be used to other nonlinear evolution equations hierarchy.

关键词：多分量C-KdV分层孤立子方程环代数积分耦合哈密顿耦合