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。     

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：     

超对称自对偶杨─Mills模型的Hamilton约化

本文研究了４维超对称自对偶杨－Ｍｉｌｌｓ模型的Ｈａｍｉｌｔｏｎ约化．在左右对称的常约束下导出了４维超对称非阿贝尔Ｔｏｄａ模型、相应的作用量以及线性系统．在主阶化下的１阶约束条件下，得到了４维超对称Ｔｏｄａ模型．本文的约化对任意李超代数都成立，并不特别要求李超代数具有纯奇素根系．     

(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：     

Lax可积系统的有限变换对称群及严格解

本文用一种简单直接的方法研究了非线性物理系统Davey-Stewartson方程及（２＋１）维的Camassa-Holm方程，并给出了它们的有限变换对称群及对称。     

超对称自对偶杨─Mills模型的Hamilton约化

本文研究了4维超对称自对偶杨-Mills模型的Hamilton约化.在左右对称的常约束下导出了4维超对称非阿贝尔Toda模型、相应的作用量以及线性系统.在主阶化下的1阶约束条件下,得到了4维超对称Toda模型.本文的约化对任意李超代数都成立,并不特别要求李超代数具有纯奇素根系.     

LCAC—SW方法中阻尼函数的研究

研究了在排列通道线性组合散射波方法中阻尼函数的衰减形式，通过计算表明，在三维Ｈ＋Ｈ２交换反应中，阻尼函数应以快于１－ｅｘｐ的形式，如ｆ（Ｒ）＝１－ｅｘｐ，在经典回转点处衰减为０，同时提出闭通道函数应分布在准经典近似不适用的区域。     

光脉冲在饱和自聚焦克尔介质中传输

综合考虑了在（２＋１）维饱和自聚焦克尔介质中光脉冲的传输问题，利用变分法得到了光脉冲在传输中的准动量，动量守恒律，利用数值法研究了初始不对称光脉冲饱和强度，耦合强度对其束宽，脉宽的影响。     

二能级系统中光场压缩与原子偶极压缩间的对称特性

揭示了共振Ｊａｙｎｅｓ-Ｃｕｍｍｉｎｇｓ模型中光场压缩与原子偶极压缩间的对称特性，并探讨了各种非线性作用包括非共振作用，虚光子过程，任意强度耦合及类Ｋｅｒ介质与腔作用对光场压缩与原子偶极压缩间的对称特性的影响，还讨论了（２ｍ＋１）量子共振下两种压缩间的内在关系     

光折变材料Cu;KNSBN的晶格振动和d—d电子跃迁

比较了铜掺杂钾钠铌酸锶钡和钾钠铌酸锶钡两样品的晶格振动和ｄ－ｄ电子跃迁谱，对于拉曼谱，Ａ１（ｚ）对称类的差别较小，Ｅ（ｘｙ）对称类的差别最大；对于红外反射谱，两对称类的均差别较大，认为Ｃｕ＾２＋部分填充了晶格Ａ位和Ｃ位，可见光范围内，ｄ－ｄ电子跃迁谱表明Ｃｕ＾２＋在晶体中形成两个深能级２．５ｅＶ和２．６４ｅＶ。     

Symmetries of (2+1)-Dimensional KQV-Ito Equation in the Bilinear Form

A set of symmetries of a generalized (2+1)-dimensional bilinear equation is given by a formal series formula. There exist four truncated symmetries for the KdV-lto model. These truncated symmetries with four arbitrary functions of time t constitute an infinite-dimensional Lie algebra which contains two types of the Virasoro subalgebra.     

Formal Series Symmetries and Truncated Symmetries of a Bilinear Schrödinger Equation

For a type of nonlinear Schrodinger equations, we get a set of formal series symmetries. For a special integrable bilinear Schrodinger equation in (2 + 1)-dimensional spacetime, some truncated symmetries which constitute an infinite dimensional Lie algebra are obtained.     

Higher-Dimensional Integrable Models with a Common Recursion Operator

Starting from any one of hereditary symmetries, we can construct a type of integrable models with arbitrary dimensions. The models with different dimensions obtained from a same hereditary symmetry possess a common recursion operator. The symmetry structures of the models are studied in their potential forms. Using the formal series symmetry approach, we can get various sets of formal series symmetries with some arbitrary functions. Generally, these sets of series symmetries are not truncated for arbitrary functions. The series symmetries wiU all be truncated if the arbitrary functions are fixed as polynomials. Some sets of nontruncated symmetries constitute generalized Virasoro algebras. The more details about the symmetries and algebras are discussed for a concrete (3+1)-dimensional KdV equation.     

Kac-Moody-Virasoro symmetry algebra of a （2＋1）-dimensional bilinear system

Based on some known facts of integrable models, this paper proposes a new （2＋1）-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable because of the existence of the higher order symmetries. The Lie point symmetries of the model constitute an infinite dimensional Kac- Moody Virasoro symmetry algebra. Making use of the infinite Lie point symmetries, the possible symmetry reductions of the model are also studied     

2+1维广义Calogero-Bogoyavlenskii-Schiff方程的无穷多对称及其约化

通过潘勒卫检验,得到了2+1维广义Calogero-Bogoyavlenskii-Schiff方程可积的条件.在这个基础上,得到了GCBS方程的双线性形式,从而根据形式级数展开法得到了无穷多对称.根据这个对称可以得到GCBS方程的约化. 关键词： 无穷多对称 截断对称 对称约化 GCBS方程     

Symmetry Algebras of Generalized (2 + 1)-Dimensional KdV Equation

Generalized symmetries with arbitrary functions of time t for the generalized (2 + 1)-dimensional KdV equation was founded by establishing a formal theory of obtaining the solution of one type of higher dimensional PDEs due to LOU (Refs [6]-[9l). These symmetries constitute an infinite dimensional Lie algebra which is a generalization to the well-known wo3 algebra. Obviously, the corresponding symmetry algebra is isomorphic to that of the Kadom tsev-Pe tviashvili (KP) equation.     

Soliton solutions and symmetries of the 2+1 dimensional Kaup–Kupershmidt equation

The 2+1 dimensional Kaup–Kupershmidt (KK) equation is considered. A bilinear form for the equation is found and then 3-soliton solutions are obtained with the assistance of Mathematica. Six symmetries of the bilinear 2+1 dimensional KK equation are given and their symmetry algebra is identified.     

Abundant Symmetry Structures of the Breaking Soliton Equation

differential equation is treated as an alternative way. For a breaking soliton equation which possesses a (1 + 1)-dimensional-like recursion operator, six sets of generalized symmetries are explicitly given. It is known that the truncated formal series symmetries of the KP and Toda equations constitute the generalized W_∞ algebra. From this paper we find that the generalized W_∞ algebra can also be realized by means of the nontruncated formal series symmetries.