一类S-mKdV方程族及其扩展可积模型

由loop代数的一个子代数出发，构造了一个线性等谱问题，再利用屠格式计算出了一类Liouvelle意义下的可积系统及其双Hamilton结构，作为该可积系统的约化，得到了著名的Schrdinger方程和mKdV方程，因此称该系统为S-mKdV方程族.根据已构造的的子代数，又构造了维数为5的loop代数的一个新的子代数，由此出发设计了一个线性等谱形式，再利用屠格式求得了S-mKdV方程族的一类扩展可积模型.利用这种方法还可以求BPT方程族、TB方程族等谱系的扩展可积模型.因此本方法具有普遍应用价值.最后作为特例，求得了著名的Schrdinger方程和mKdV方程的可积耦合系统.     

AKNS方程族的一类扩展可积模型

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,求得了KdV方程和MKdV方程的可积耦合 关键词： 可积耦合 loop代数 AKNS方程族     

推广的一类Lie代数及其相关的一族可积系统

对已知的Lie代数An-1作直接推广得到一类新的Lie代数gl(n,C).为应用方便，本文只考虑Lie代数gl(3,C)情形.构造了gl(3,C)的一个子代数，通过对阶数的规定，得到了一类新的loop代数.作为其应用，设计了一个新的等谱问题，得到了一个新的Lax对.利用屠格式获得了一族新的可积系统，具有双Hamilton结构,且是Liouville可积系.作为该方程族的约化情形，得到了新的耦合广义Schrdinger方程. 关键词： Lie代数 可积系 Hamilton结构     

耦合的AKNS-Kaup-Newell孤子方程族的一类可积扩展模型

基于Lie圈代数?1的子代数建立了一个等谱问题，导出了耦合的AKNS- Kaup- Newell孤子方程族。另外，利用扩展相应Lie代数于?2的方法，建立了该方程族的可积扩展模型，即可积耦合。     

高维微分-差分模型的Virasoro对称子代数，多线性变量分离解和局域激发模式

寻找高维可积模型是非线性科学中的重要课题.利用无穷维Virasoro对称子代数［σ(f₁),σ(f₂)］=σ(f′₁f₂-f′₂f₁)和向量场的延拓结构理论，能够得到各种高维模型.选取一些特殊的实现，可以给出具有无穷维Virasoro对称子代数意义下的高维微分可积模型.把该方法推广到微分-差分模型上，构造出具有弱多线性变量分离可解性的(3+1)维类Toda晶格.另外，该模型的一个约化方程为具有多线性变量分离可解性的(2+1)维特殊Toda晶格.连续运用对称约化方法可以得到此特殊Toda晶格的一个(1+1)维约化方程具有多线性变量分离可解性.因为得到的精确解里含有低维任意函数，从而可以构造出丰富地局域激发模式，如dromion解，lump解，环孤子解，呼吸子解，瞬子解，混沌斑图和分形斑图等等. 关键词： Virasoro代数 微分-差分模型 变量分离 局域激发模式     

NO(X2∏1/2,3/2)v=1←0塞曼跃迁谱及其特性研究

根据塞曼效应理论和激光磁共振光谱技术(LMR)的基本原理,讨论了双原子分子²∏态的塞曼效应特性并导出了解释分子塞曼跃迁的简明代数拟合方程,用这些方程对¹⁴N¹⁶O(X²∏_1/2.3/2)及¹⁵N¹⁶O(X²∏_3/2)(v=1←0)的LMR谱线进行数据拟合,得到塞曼跃迁上、下子能级的g_J因子值和二级塞曼效应因子k₂.将按Hund耦合情形(a)及过渡情形(ab)的理论和拟合方程计算出的磁场位置分别与实验结果相比较,结果表明对NO分子而言,过渡情形(ab)能较真实反映它的耦合情况,且在较高强度磁场下,必须计及二级塞曼修正验证了采用上述代数拟合方程实现新分子LMR谱线标识和指认的可靠性,并提供了系统的处理方法.     

(2+1)维离散型Toda方程的对称性

将文献[1—4]提出的形式级数对称理论推广应用到(2+1)维的离散型Toda方程,得到了二族无穷多广义截断对称。每一族对称构成一个广义W_∞代数,通常的W_∞代数仅是这个代数的子代数。 关键词：     

超导临界温度理论(Ⅲ)

本文定出超导临界温度T_c级数公式(1)的前几项系数。对于形式为α²F(ω)=(λω)/2[a₁δ(ω-ω₁)+(1-a₁)δ(ω-ω₂)]的双δ型有效声子谱及若干具体材料的谱,将级数公式计算的T_c与Allen-Dynes公式(以下简称A-D公式)及Eliashberg方程的数值解作了比较。计算表明,当级数(1)收敛时,级数公式计算的结果较A-D公式更接近于数值解。此外,本文还给出了一个近似的T_c级数公式,得到了估计该T_c级数收敛半径的方法,并计算了若干材料的收敛半径值。因此,可估计级数公式(1)的适用范围。 关键词：     

钠米Al2O3块体材料在可见光范围的荧光现象

对不同温度退火未掺Ｃｒ的纳米结构Ａｌ₂Ｏ₃块体的荧光谱进行了系统的研究。结果表明，在纳米级勃母石，η－Ａｌ₂Ｏ₃和γ－Ａｌ₂Ｏ₃试样中均观察到两个宽的荧光带（ｐ₁和ｐ₂带），它们的波数范围分别为２００００—１４５００和１４５００—１１５００ｃｍ^－１。ｐ₁带可归结为纳米Ａｌ_{2关键词：}     

超声冷却SO2( 1A2— 1A1)激光诱导荧光激发谱的转动分析

通过改变SO₂/Ar配比，研究了超声膨胀冷却SO₂( ¹A₂— ¹A₁)系统315—330nm波段振动分辨的激光诱导荧光(LIF)激发谱.获得了属于两个完整带系(1,m,1),(0,n,1)—(0,0,0)的高分辨转动结构谱.其中(ν′₁,ν′₂,ν′₃)=(0,9,1),(0,10,1),(1,7,1),(1 关键词：     

Multi-component Dirac equation hierarchy and its multi-component integrable couplings system

A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M-dimensional loop algebra \tilde{X} is produced. By taking advantage of \tilde{X}, a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra \tilde{F}_M of the loop algebra \tilde{X} is presented. Based on the \tilde{F}_M, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.     

Two types of loop algebras and their expanding Lax integrable models

Though various integrable hierarchies of evolution equations were obtained by choosing proper U in zero-curvature equation U_t-V_x+[U,V]=0, but in this paper, a new integrable hierarchy possessing bi-Hamiltonian structure is worked out by selecting V with spectral potentials. Then its expanding Lax integrable model of the hierarchy possessing a simple Hamiltonian operator \widetilde{J} is presented by constructing a subalgebra \widetilde{G } of the loop algebra \widetilde A₂. As linear expansions of the above-mentioned integrable hierarchy and its expanding Lax integrable model with respect to their dimensional numbers, their (2+1)-dimensional forms are derived from a (2+1)-dimensional zero-curvature equation.     

The multi-component Tu hierarchy of soliton equations and its multi-component integrable couplings system

A new simple loop algebra GM is constructed, which is devoted to the establishing of an isospectral problem. By making use of the Tu scheme, the multi-component Tu hierarchy is obtained.Furthermore, an expanding loop algebra FM of the loop algebra GM is presented. Based on the FM, the multi-component integrable coupling system of the multi-component Tu hierarchy has been worked out. The method can be applied to other nonlinear evolution equation hierarchies.     

The generalized nonlinear Schrödinger hierarchy, its integrable coupling system and their bi-Hamiltonian structure

Based on a subalgebra G of Lie algebra A₂, a new Lie algebra G^∗ is constructed. By making use of the Tu scheme, the generalized nonlinear Schrödinger hierarchy and its integrable coupling are both obtained with the help of their corresponding special loop algebras. At last, by means of the quadratic-form identity, their bi-Hamiltonian structures of the generalized nonlinear Schrödinger hierarchy and its integrable coupling system are worked out respectively. The approach presented in this Letter can be used in other integrable hierarchies.     

A new integrable case of the motion of the 4-dimensional rigid body

A Lax pair for a new family of integrable systems on SO(4) is presented. The construction makes use of a twisted loop algebra of theG ₂ Lie algebra. We also describe a general scheme producing integrable cases of the generalized rigid body motion in an external field which have a Lax representation with spectral parameter. Several other examples of multi-dimensional tops are discussed.     

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

A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is A1 as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multi-component 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.     

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

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.     

A Class of New Lie Algebra,the Corresponding g-mKdV Hierarchy and Its Hamiltonian Structure

A class of new Lie algebra B ₃ is constructed, which is far different from the known Lie algebra A _n−1. Based on the corresponding loop algebra [(B₃)\tilde]\tilde{B_{3}}, the generalized mKdV hierarchy is established. In order to look for the Hamiltonian structure of such integrable system, a generalized trace functional of matrices is introduced, whose special case is just the well-known trace identity. Finally, its expanding integrable model is worked out by use of an enlarged Lie algebra.     

An integrable Hamiltonian hierarchy, a high-dimensional loop algebra and associated integrable coupling system

A subalgebra of loop algebra ?_2 is established. Therefore, a new isospectral problem is designed. By making use of Tu's scheme, a new integrable system is obtained, which possesses bi-Hamiltonian structure. As its reductions, a formalism similar to the well-known Ablowitz－Kaup－Newell－Segur (AKNS) hierarchy and a generalized standard form of the Schr?dinger equation are presented. In addition, in order for a kind of expanding integrable system to be obtained, a proper algebraic transformation is supplied to change loop algebra ?_2 into loop algebra ?_1. Furthermore, a high-dimensional loop algebra is constructed, which is different from any previous one. An integrable coupling of the system obtained is given. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented.