（2+1）维NLBQ方程和KP方程的多dromion结构和相互作用的研究

从（2+1）维双线性形式的非局域Bussinesq(NLBQ)方程和KP方程的隐线孤子解出发,可以找到与某种势所相应的各方向都指数衰减的dromion解.利用图形分析的方法,对这些dromion之间的相互作用进行了详细的研究.发现这两种模型中的dromion间的相互作用只引起位相漂移,不引起形状和速度的变化,也不引起旋转.即dromion间的相互作用是弹性的,没有能量、动量和角动量的交换. 关键词：     

(2+1)-DIMENSIONAL DERIVATIVE NONLINEAR SCHRODINGER EQUATION

A(2+1)-dimensional multi-component derivative nonlinear Schr?dinger (DNLS) equation is obtained from the symmetry constraint of the modified Kadomtsev-Petviashvili equation, The model is proved to be inte- grable under the meaning that it possesses the Paitdevé property and the infinitely many generalized symmetries which constitute a generalized W_∞ algebra, An integrable DNLS hierarchy is obtained from the flow equation of infinitely many symntetries of the DNLS equation.     

SIMILARITY REDUCTIONS OF THE (2+1)-DIMENSIONAL BURGERS SYSTEM

In this paper, using the direct method of the (2+1)-dimensional multi-component Burgers system, some types of similarity reductions are obtained. The corresponding group explanations of the reductions, Virasoro integrability and soliton solutions of Burgers system are also discussed.     

一个4+1维宇宙模型

我们讨论的4+1维宇宙模型是通常的四维时空和一个紧致的一维内禀空间的直积空间。我们假定四维时空的能量密度是以辐射为主的,而内禀子空间的能动张量是一个阶跃函数。通过求解五维的Einstein场方程得到前四维时空由de-Sitter解过渡到标准模型的辐射为主解,与此同时内禀子空间的尺度由减幅振荡过渡到为按t的负幂次收缩而趋于一常量。 关键词：     

A SOLVABLE 1+1-DIMENSIONAL U(1) GAUGE THEORY

A 1+1-dimensional U(1+1) gauge theory is proposed and the exact solution of its spectrum and corresponding energy eigenstates is found.     

CLASSIFICATION OF (n + 2)-DIMENSIONAL METRIC n-LIE ALGEBRAS

In this paper, we give the classification of (n + 2)-dimensional metric n-Lie algebras in terms of some facts about n-Lie algebras.     

(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：     

THE CRITERION FOR FRACTIONAL CHARGE OF(1+1)-DIMENSIONAL DIRAC FIELD

The fractional fermion number (charge) of (1+1)-dimensional Dirac field interacting with a scalar background field is investigated. By means of the correspondence principle in (1+1)-dimensional field theory,it is shown that only when the background field develops a solitvn with a node can the fractional fermion number be induced(node theorem).Consistently, a zero mode bound state of the fermion field should be present and responsible for the fractional charge as long as the soliton satisfies certain conditions (theorem of zero mode).We have also obtained the analytical expression of the vacuum charge distribution in the vicinitu of distorted reqion.     

THE EXACT SOLUTIONS OF THE BURGERS EQUATION AND HIGHER-ORDER BURGERS EQUATION IN (2+1) DIMENSIONS

Some exact solutions of the Burgers equation and higher-order Burgers equation in (2+1) dimensions are obtained by using the extended homogeneous balance method. In these solutions there are solitary wave solutions, close formal solutions for the initial value problems of the Burgers equation and higher-order Burgers equation, and also infinitely many rational function solutions. All of the solutions contain some arbitrary functions that may be related to the symmetry properties of the Burgers equation and the higher-order Burgers equation in (2+1) dimensions.     

A MONTE CARLO RENORMALIZATION GROUP STUDY OF A 2-DIMENSIONAL TRIANGULAR LATTICE

The method developed by D.J.E.Callaway is applied to Ising model on a two-dimensional triangular lattice. A fixed point and critical exponent are found. The results are consistent with one of the exact theories very well. Obviously this method show superiority to that obtained by some other approximate methods. The method is also applied to Z₂ gauge theory on a 2-dimensional triangular lattice, no fixed points are found, in agreement with other methods.     

A(1+1)-DIMENSIONAL LATTICE U(1) GAUGE MODEL AND THE FERMION SPECIES DOUBLING

A(1+1)-dimensional lattice U91) gauge model with fermion species doubling is solved exactly.The results show that doubling exists for meson states composed of fermions and antifermions.Furthermore we prove that Susskind fermions can beat the doubling of meson states.     

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。     

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。     

ABUNDANT DROMION-LIKE STRUCTURES TO THE (2+1) DIMENSIONAL KdV EQUATION

The abundant generalized dromion structures for the (2+1)-dimensional KdV equation are obtained using the homogeneous balance method. We give not only the general curve soliton which is finite on a curved line and localized apart from the curve, find but also the dromion solutions which can be driven by two perpendicular line soliton and by two non-perpendicular line soliton and by one line soliton and one curve line soliton. Various types of multi-dromion solutions can be constituted by selecting different arbitrary functions of y. The (1+N) dromion obtained by Radha et al.^[3] is only a very special case of our results.     

(2+2)RESONANCE-ENHANCED MULTIPHOTON IONIZATION-FRAGMENTATION STUDY OF DIMETHYLAMINE

The multiphoton ionization spectra of dimethylamine are given in the 445-470 nm region. A time of flight mass spectrometer was used,and experiment was done under collision free condition. It is found that (2+2) resonance enhanced multiphoton ionization through (n_N,3s) Rydberg state produces parent ions which endure pseudo-α and C—N bond cleavages. The former forms CH₃N⁺H=CH₂ ions,and the latter gives CH₂=N⁺H₂ ions .     

激光等离子体相互作用的2(1/2)维粒子模拟程序

研制了2(1/2)维粒子模拟程序PLASIM(Plasma Simulator),介绍经过验证的该粒子模拟程序的算法,其特点是自含碰撞,即β粒子云模型的选取使得该程序无需额外的计算开销就能在程序中自洽地含有碰撞,使计算结果更加符合实际情况.另外电子和离子的运动都是相对论的,适于模拟超强激光与等离子体的相互作用.     

具有无穷维Virasoro型对称代数的(3+1)维可积模型

利用无中心的Virasoro型对称李代数[σ(f₁(t)),σ(f₂(t))] =σ(f₁f₂-f₂f₁)的每一个实现，能得到各种高维模型．通过一些特殊实现，给出了具有Virasoro型对称代数意义下的许多（3+1）维可积模型     

(2+2)RESONANCE ENHANCED MULTIPHOTON IONIZATION-FRAGMENTATION STUDY OF DIMETHYLAMINE

The multiphoton ionization spectra of dimethylamine are given in the 445-470 nm region. A time of flight mass spectrometer was used,and experiment was done under collision free condition. It is found that (2+2) resonance enhanced multiphoton ionization through (n_N,3s) Rydberg state produces parent ions which endure pseudo-α and C—N bond cleavages. The former forms CH₃N⁺H=CH₂ ions,and the latter gives CH₂=N⁺H₂ ions .     

三维SPH程序及其在斜高速碰撞问题的应用

叙述了平滑粒子流体动力学(简称SPH)的基本概念,重新推导了所用的基本方程。介绍了具体计算格式、算法以及策略等。对所编制的程序作了一定的检验。对SPH方法中的人为粘性和人为热流的作用作了数值考查。还提供了一个三维高速碰撞现象的算例。最后指出尚存在的若干问题。     

THE CORRESPONDENCE PRINCIPLE IN (1+1)-DIMENSIONAL FIELD THEORY AND THE COLEMAN THEOREM

The correspondence relations between a fermion field and a boson field in (1+1)-dimensional quantum field theory is discussed in general. Emphases have been laid on the renorinalization with respect.to an arbitrary mass parameter in boson version as well as the nonlocal property of currents in fermion version. After establishing the equivalence between the continuous chiral transformation in fermion version and the translational transformation in boson version, we are able to prove the Coleman theorem correspondingly.