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Induced lie algebras of a Six-Dimensional Matrix lie algebra

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Communications in Theoretical Physics 2008年第8期50卷 289-294页

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

By using a six-dimensional matrix lie algebra [*** and ***,***.A 360 (2006) 92], three induced lie algebras are *** of them is obtained by extending lie bracket,the others are higher- dimensional complex lie algebras constructed by using linear *** equivalent lie algebras of the later two with multi-component forms are obtained as *** their applications,we derive an integrable coupling and quasi-Hamiltonian structure of the modified TC hierarchy of soliton equations.

关键词： lie algebra soliton equation Hamiltonian structure

Symmetries and Their lie algebra of a Variable Coefficient Korteweg-de Vries Hierarchy

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Chinese Annals of Mathematics,Series B 2016年第4期37卷 543-552页

作者： Xiaoying ZHU Dajun ZHANG College of Sciences Shandongjianzhu University Department of Mathematics Shanghai University

IsospectrM and non-isospectral hierarchies related to a variable coefficient Painlev6 integrable Korteweg-de Vries （KdV for short） equation are derived. The hier- archies share a formal recursion operator which is not a rigorous recursion operator and contains t explicitly. By the hereditary strong symmetry property of the formal recur- sion operator, the authors construct two sets of symmetries and their lie algebra for the isospectral variable coefficient Korteweg-de Vries （vcKdV for short） hierarchy.

关键词： vcKdV hierarchies Symmetries lie algebra

lie Triple Derivations of the lie algebra of Dominant Block Upper Triangular Matrices

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algebra Colloquium 2018年第3期25卷 475-492页

作者： Prakash Ghimire Huajun Huang Department of Mathematics and Physical Sciences LSU of Alexandria Alexandria LA 71302 USA Department of Mathematics and Statistics Auburn University Auburn AL 36849 USA

Let N be the lie algebra of all n x n dominant block upper triangular matrices over a field F. In this paper, we explicitly describe all lie triple derivations of N when char（F） ≠ 2. As an application, we character... 详细信息

关键词： lie triple derivation block upper triangular matrix lie algebra

A Corresponding lie algebra of a Reductive homogeneous Group and Its Applications

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Communications in Theoretical Physics 2015年第5期63卷 535-548页

作者：张玉峰吴立新芮文娟 College of Sciences China University of Mining and Technology School of Environment Science and Spatial Informatics China University of Mining and Technology

With the help of a lie algebra of a reductive homogeneous space G/K, where G is a lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding （2＋1）-dimensional integrable hierarchy is obtained by applying the binormial-residue representation （BRR） method, whose ttamiltonian structure is derived from the trace identity for deducing （2＋1）-dimensional integrable hierarchies, which was proposed by Tu, et al. We further consider some reductions of the expanding integrable hierarchy obtained in the paper. The first reduction is just right the （2＋1 ）-dimensionai AKNS hierarchy, the second-type reduction reveals an integrable coupling of the （2＋1）-dimensional AKNS equation （also called the Davey-Stewartson hierarchy）, a kind of （2＋1）-dimensionai Sehr6dinger equation, which was once reobtained by Tu, Feng and Zhang. It is interesting that a new （2＋1）-dimensional integrable nonlinear coupled equation is generated from the reduction of the part of the （2＋1）-dimensional integrable coupling, which is further reduced to the standard （2＋1）-dimensionaJ diffusion equation along with a parameter. In addition, the well-known （1＋1）-dimensional AKNS hierarchy, the （1＋1）-dimensional nonlinear Schr6dinger equation are all special cases of the （2＋1）-dimensional expanding integrable hierarchy. Finally, we discuss a few discrete difference equations of the diffusion equation whose stabilities are analyzed by making use of the yon Neumann condition and the Fourier method. Some numerical solutions of a special stationary initial value problem of the （2＋1）-dimensional diffusion equation are obtained and the resulting convergence and estimation formula are investigated.

关键词： (2+1)-dimensional hierarchy lie algebra Hamiltonian structure

A New lie algebra and a Way to Generate Multiple Integrable Couplings

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Communications in Theoretical Physics 2007年第12期48卷 979-982页

作者： FENG Bin-Lu~(1,2)and HAN Bo~1~1 Department of Mathematics,Harbin Institute of Technology,Harbin 150001,China~2 Department of Mathematics,Weifang University,Weifang 261000,China Department of Mathematics Harbin Institute of Technology Harbin 150001 China Department of Mathematics Weifang University Weifang 261000 China

A new higher-dimensional lie algebra is constructed,which is used to generate multiple integrable *** this,we come to a general approach for seeking multi-integrable couplings of the known integrablesoliton equations.

关键词： lie algebra integrable hierarchy Hamiltonian structure

A New lie algebra and Its Related Liouville Integrable Hierarchies

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Communications in Theoretical Physics 2010年第9期54卷 407-411页

作者：王惠王新赠刘国栋杨记明 Department of Mathematics Shanghai University College of Information Science and Engineering Shandong University of Science and Technology

A new lie algebra G and its two types of loop algebras G1 and G2 are constructed. Basing on G1 and G2, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obtained respectively under the framework of zero curvature equation, which is derived from the compatibility of the isospectral problems expressed by Hirota operators. At the same time, we obtain the Hamiltonian structure of the first hierarchy and the bi-Hamiltonian structure of the second one with the help of the quadratic-form identity.

关键词： lie algebra Liouville integrable hierarchy Hirota operator Quadratic-form identity

ONEOptimal:A Maple Package for Generating One-Dimensional Optimal System of Finite Dimensional lie algebra

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Communications in Theoretical Physics 2014年第2期61卷 160-170页

作者：苗倩胡晓瑞陈勇 Shanghai Key Laboratory of Trustworthy Computing East China Normal University

We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional lie algebra for nonlinear equations automatically based on Olver's theory. The core of this theory is viewing the Killing form of the lie algebra as an invariant for the adjoint representation. Some examples are given to demonstrate the validity and efficiency of the program.

关键词： group-invariant solutions optimal system group classification lie algebra symbolic computation

The q-Analog Klein Bottle lie algebra

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algebra Colloquium 2014年第4期21卷 561-574页

作者： Cuipo Jiang Jingjing Jiang Yufeng Pei Department of Mathematics Shanghai diaotong UniversityShanghai 200240 China Department of Mathematics Shanghai Normal University Shanghai 200234 China

In this paper, we study an infinite-dimensional lie algebra Bq, called the q-analog Klein bottle lie algebra. We show that Bq is a finitely generated simple lie algebra with a unique （up to scalars） symmetric invari... 详细信息

关键词： lie algebra Klein bottle invariant bilinear form central extension derivation

Upper Triangular Matrix of lie algebra and a New Discrete Integrable Coupling System

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Communications in Theoretical Physics 2007年第3期47卷 393-396页

作者： YU Fa-Jun ZHANG Hong-Qing Department of Applied Mathematics Dalian University of Technology Dalian 116024 China

The upper triangular matrix of lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice soliton equation spectral problem is obtained and leads to a novel hierarchy of the nonlinear lattice equation hierarchy. It indicates that the study of integrable couplings using upper triangular matrix of lie algebra is an important step towards constructing integrable systems.

关键词： upper triangular matrix lie algebra integrable coupling system