Kaup-Kupershmidt方程的对称代数

利用Ｍｉｕｒａ变换和Ｃｏｌｅ－Ｈｏｐｆ变换，证明了Ｋａｕｐ－Ｋｕｐｅｒｓｈｍｉｄｔ方程的１０族时间无关对称构成一个非Ａｂｅｌ李代数。与１０族对称相应的１０族方程具有共同的强对称，１０族可积模型的时间无关对称及其构成的李代数亦被给定。     

2＋1维双线性Sawada—Kotera方程的对称结构

对一类２＋１维双线性方程从两个不同程度建立了形式级数对称理论。从一已知的时间无关对称出发或从与一维空间坐标有关的任意函数发出，均可得到了包含时间任意函数的形式级数对称。对于２＋１维双线性Ｓａｗａｄａ－Ｋｏｔｅｒａ方程，存在６个载断对称。这些截断对称构成一无究维李代数。一些有意义的子代数（如Ｖｉｒａｓｏｒｏ代数等）也被给定。     

2+1维双线性Sawada-Kotera方程的对称结构

对一类２＋１维双线性方程从两个不同角度建立了形式级数对称理论。从一已知的时间无关对称出发或从与一维空间坐标有关的任意函数出发，均可得到一包含时间任意函数的形式级数对称。对于２＋１维双线性Ｓａｗａｄａ－Ｋｏｔｅｒａ方程，存在６个截断对称。这些截断对称构成一无穷维李代数。一些有意义的子代数（如Ｖｉｒａｓｏｒｏ代数等）也被给定。     

耦合Burgers系统的Painlevé性质分析，对称和对称约化

本文给出了耦合Burgers系统的Painlevé性质，逆强对称算子，无穷多对称和李对称约化。通过把强对称和逆强对称算子重复多次作用到耦合Burgers模型的一些平庸对称，如恒等变换，空间平移变换和标度变换上，我们得到了三族无穷多对称。这些对称构成了无穷维李代数。用其中的有限维子代数——点李代数对模型进行对称约化，得到了模型的群不变解。     

非线性2+1维Khokhlov-Zabolotskaya方程的无穷多对称及其代数结构

对于2+1维的可积的Khokhlov-Zabolotskaya方程,利用形式级数对称的方法,得到了一包含无穷多任意时间函数的无穷多截断对称。由这些对称构成的无限维李代数是W_(?)代数的推广。 关键词：     

(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：     

super—Gel‘fand—Dickey算子,Backlund Darboux变换及对称

给出了ｓｕｐｅｒ－Ｇｅｌ’ｆａｎｄ－Ｄｉｃｋｅｙ算子的Ｋｕｐｅｒｓｃｈｉｍｄｔ－Ｗｉｌｓｏｎ辅助动力学变量的行列式表示形式。利用算子分解导出了ｓｕｐｅｒ－Ｇｅｎｅｒａｌｉｚｅｄ－ＫｄＶ方程２ｎ－１个Ｂａｃｋｌｕｎｄ－Ｄａｒｂｏｕｘ变换及对应的对称的精确形式。     

微重坏境下旋转对称贮箱内静液面方程Runge-Kutta数值解

由力学平衡方程导出了旋转对称贮箱内静液面的二阶非线性常微分方程，接着具体了球腔，旋转 椭球腔、柱面腔的边界接触角条件，最后使用Ｒｕｎｇｅ－Ｋｕｔｔａ法在计算机上得出了数值结果，绘出静液面开头曲线，分析了算法特点。     

钠5S态与基态钾原子的碰撞能量转移

在Ｎａ－Ｋ混合蒸汽中，利用染料激光器，将基态Ｎａ原子双光子激发到５Ｓ态。用荧光法测量了过程Ｎａ（５Ｓ）＋Ｋ（４Ｓ）→Ｎａ（３Ｓ）＋Ｋ（８Ｄ，１０Ｓ）的碰撞转移截面，Ｋ８Ｄ，１０Ｓ对Ｎａ５Ｓ的荧光比中，含有Ｋ８Ｄ１０Ｓ碰撞转移的影响。第２个实验可以消除这个影响，双光子激发Ｋ原子到８Ｄ（或１０Ｓ）探测８Ｄ（１０Ｓ）对１０Ｓ（８Ｄ）的荧光比，Ｎａ（５Ｓ）→Ｋ（８Ｄ，１０Ｓ）碰撞转移截面（１０－１５ｃｍ２）分别是１０．５±４．２和９．５±３．８     

超主手征场模型中的无穷保形对称性和Riemann-Hilbert变换

我们在超主手征场模型中找到了一种新的对称变换——C变换,发现在这种变换下体系具有一个与没有中心项的Virasoro代数相关的无穷维李代数.利用Riemann-Hilbert变换,我们探讨了C变换的物理根源.     

Nonlocal symmetries of Plebański’s second heavenly equation

We study nonlocal symmetries of Plebański’s second heavenly equation in an infinite-dimensional covering associated to a Lax pair with a non-removable spectral parameter. We show that all local symmetries of the equation admit lifts to full-fledged nonlocal symmetries in the infinite-dimensional covering. Also, we find two new infinite hierarchies of commuting nonlocal symmetries in this covering and describe the structure of the Lie algebra of the obtained nonlocal symmetries.     

Loop Algebra of Lie symmetries for a short-wave equation

It is demonstrated that Lie point symmetries associated with a nonlinear equation for short waves in three dimensions generate an infinite-dimensional Lie algebra—a loop Algebra. Classification of the independent sets of the subalgebra is done through the adjoint action of the corresponding generators. Different forms of similarity solutions are discussed.     

Additional symmetries and string equations of the noncommutative B and C type KP hierarchies

In this paper, we construct the noncommutative B and C type KP hierarchies using pseudo-differential operators and reducing conditions. Further a series of additional flows of the noncommutative B and C type KP hierarchies will be defined and the additional symmetries constitute the B and C type infinite dimensional Lie algebra W_1+∞. In addition, the generating function of the additional symmetries can also be proved to have a nice form in terms of wave functions. Further, the string equations of the noncommutative B and C type KP hierarchies are derived.     

New symmetries for the Ablowitz–Ladik hierarchies

In the Letter we give new symmetries for the isospectral and non-isospectral Ablowitz–Ladik hierarchies by means of the zero curvature representations of evolution equations related to the Ablowitz–Ladik spectral problem. Lie algebras constructed by symmetries are further obtained. We also discuss the relations between the recursion operator and isospectral and non-isospectral flows. Our method can be generalized to other systems to construct symmetries for non-isospectral equations.     

NEW SYMMETRIES AND LIE ALGEBRAS OF THE GENERAL KdV EQUATION

The strong symmetry of the general KdV equation is factorized to a simple form and then the inverse strong symmetry is obtained explicitly. Acting a strong symmetry of the general KdV equation on the trivial symmetry and the known re symmetry, we obtain four new sets of symmetries of the general KdV equation. All these sets of symmetries constitute an infinite dimensional Lie algebra.     

Symmetries and Similarity Reductions of Nonlinear Diffusion Equation

The inverse recursion operator, three new sets of symmetries, and infinite-dimensional Lie algebras for the nonlinear diffusion equation are given. Some nonlocal symmetries related to eigenvectors of the recursion operator with the eigenvalue λi are also obtained with the help of the recursion operator φi=φ-λi. Using a part of these symmetries we get twelve types of nontrivial new similarity reduction.     

微扰Kepler系统轨道微分方程的近似Lie对称性与近似不变量

把极角θ视为独立变量,得到Kepler系统的轨道微分方程.首先讨论Kepler系统轨道微分方程的Lie对称性和不变量,微扰Kepler系统轨道微分方程的精确Lie对称性和精确不变量,其次讨论微扰Kepler系统轨道微分方程的近似Lie对称性和近似不变量,并得到了微扰Kepler系统的9个一阶近似Lie对称性和6个一阶近似不变量,其中1个实为精确不变量,而其余5个分别等于微扰系数ε乘以Kepler系统相应的5个不变量。     

Lie Symmetry Analysis and Conservation Laws of a Generalized Time Fractional Foam Drainage Equation

In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann-Liouville derivative, the Lie point symmetries and symmetry reductions of the equation are derived, respectively. Furthermore, conservation laws with two kinds of independent variables of the equation are performed by making use of the nonlinear self-adjointness method.