中心为4的8维幂零李代数的分类

In this paper, we give a complete classification of eight dimensional nilpotent Lie algebras with four-dimensional center by using the method of Skjelbred and Sund.     

Bijective 1-Cocycles and Classification of 3-Dimensional Left-Symmetric Algebras

Left-symmetric algebras have close relations with many important fields in mathematics and mathematical physics. Their classification is very complicated due to the nonassociativity. In this article, we re-study the correspondence between left-symmetric algebras and the bijective 1-cocycles. Then a procedure is provided to classify left-symmetric algebras in terms of classification of equivalent classes of bijective 1-cocycles. As an example, the 3-dimensional complex left-symmetric algebras are classified.     

新(2+1)-维超可积系统的生成

本文利用二项式残数表示方法生成(2+1)-维超可积系统. 由这些系统得到了一个新的(2+1)-维超孤子族,它能约化为(2+1)-维超非线性Schrodinger方程. 特别地,我们得到两个具有重要物理应用的结果,一个是(2+1)-维超可积耦合方程,另一个是(2+1)-维的扩散方程. 最后借助超迹恒等式给出了新(2+1)-维超可积系统的Hamilton结构.     

(2+1)-维破裂孤子方程的群叶状方法和显式解

利用等变活动标架理论,研究(2+1)-维破裂孤子方程的群叶状方法和显式解.原方程的对称群的无穷维部分被用来产生整个解空间的叶状结构,于是分解系统就继承了对称群的有限维部分.求解的过程完全符号化和算法化.利用群叶状方法,破裂孤子方程的一些显式精确解被得到,这些解关于无穷维对称子群封闭.     

LIE SYMMETRY ANALYSIS AND PAINLEV(E) ANALYSIS OF THE NEW (2+1)-DIMENSIONAL KdV EQUATION

Lie point symmetries associated with the new (2 l)-dimensional KdV equation ut 3uxuy uxxy = 0 are investigated. Some similarity reductions are derived by solving the the soliton solution is obtained directly from the B(a)cklund transformation.     

两类(2+1)维可积系统

利用一个广义等谱问题的相容性得到了一个广义零曲率方程.作为其应用,首先利用loop代数设计了两个广义等谱问题,然后利用零曲率方程导出了两类(2+1)维Lax可积系统.     

Group-Invariant Solutions and Conservation Laws of One-Dimensional Nonlinear Wave Equation

Based on classical Lie symmetry method, the one-dimensional nonlinear wave equation is investigated. By using four-dimensional subalgebras of the equation, the invariant groups and commutator table are constructed. Furthermore, optimal system of the equation is obtained, and the exact solutions can be gained by solving reduced equations. Finally, a complete derivation of the conservation law is given by using conservation multipliers.     

Classification of Finite Factor Representations of the (2m+1)-Dimensional Heisenberg Group over a Countable Field of Finite Characteristic

For a field F that is the direct limit of an increasing chain of finite fields, we describe the Bratteli diagram, the finite complex factor representations, the Plancherel formula, and the projective modules of the corresponding Heisenberg group.     

用改进的代数方法构造(2+1)维ZK-MEW方程的精确行波解

利用一种改进的统一代数方法将构造(2+1)维ZK MEW((2+1)-dimensionalZakharov-Kuznetsovmodifiedequalwidth)方程精确行波解的问题转化为求解一组非线性的代数方程组．再借助于符号计算系统Mathematica求解所得到的非线性代数方程组,最终获得了方程的多种形式的精确行波解．其中包括有理解,三角函数解,双曲函数解,双周期Jacobi椭圆函数解,双周期Weierstrass椭圆形式解等．并给出了部分解的图形.     

关于(2+1)-维色散的长波方程求解的一个注记

在文献[3]的基础上，根据一些简单方程的特征，导出了(2十1)—维色散的长波方程的新的精确解，其中包含了已有文献中的孤子解，多孤子解等．     

KdV-Burgers方程的对称与孤子解

考虑KdV-Burgers方程的一些简单对称及其构成的李代数,并利用对称约化方法将KdV-Burgers方程化为常微分方程,从而得到该方程的群不变解.此外,利用多项式展开式的方法去获得KdV-Burgers方程的新的孤子波解.     

A （2＋1）-Dimensional Dispersive Long Wave Hierarchy and its Integrable Couplings

Under the frame of the (2 1)-dimensional zero curvature equation and Tu model, the (2 1)-dimensional dispersive long wave hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one. Moreover, a class of integrable coupling system for dispersive long wave hierarchy and (2 1)-dimensional multi-component integrable system will be investigated.     

Symmetries in (1+1)-dimensional Integrable System with Their Algebraic Structures and Conserved Quantities

In this paper we offer a general method or constructing symmetries and conserved quantities in the (1 + 1)-dimensional integrable system, prove the algebraic relations between symmetries, and what is more, give applications of this method in many integrable systems with physical significance.     

Riccati方程与(2+1)维非线性物理模型的分离变量解

对于(2+1)维非线性物理模型,欲获其解并非易事.本文试图在变量分离法中,通过设定的R iccati方程来得到方程的解.同时,以(2+1)维Bo iti-L eon-M anna-P em p inelli方程和Burgers方程为例来说明之.     

Systems of second-order linear ODE’s with constant coefficients and their symmetries II. The case of non-diagonal coefficient matrices

We complete the analysis of the symmetry algebra L for systems of n second-order linear ODEs with constant real coefficients, by studying the case of coefficient matrices having a non-diagonal Jordan canonical form. We also classify the Levi factor (maximal semisimple subalgebra) of L, showing that it is completely determined by the Jordan form. A universal formula for the dimension of the symmetry algebra of such systems is given. As application, the case n = 5 is analyzed.     

LIE SYMMETRY ANALYSIS AND PAINLEVE ANALYSIS OF THE NEW(2+l)-DIMENSIONAL KdV EQUATION

Lie point symmetries associated with the new (2 1)-dimensional KdV equation ut 3uxuy uxxy= 0 are investigated. Some similarity reductions are derived by solving the corresponding characteristic equations. Painleve analysis for this equation is also presented and the soliton solution is obtained directly from the Backlund transformation.     

热方程的非古典势对称群与不变解

主要研究了热方程与波方程的非古典势对称群生成元及相应的群不变解．研究表明对于守恒形式的偏微分方程,可通过其伴随系统求得的非古典势对称群生成元来构造其显式解．这些显式解不能由方程本身的Lie对称群生成元或Lie-B?cklund对称群生成元构造得到．     

A symmetry classification for a class of (2+1)-nonlinear wave equation

In this paper, a symmetry classification of a (2+1)-nonlinear wave equation u_tt−f(u)(u_xx+u_yy)=0 where f(u) is a smooth function on u, using Lie group method, is given. The basic infinitesimal method for calculating symmetry groups is presented, and used to determine the general symmetry group of this (2+1)-nonlinear wave equation.