非线性耦合标量场方程的精确解

在非线性耦合标量场方程已有精确解基础上，利用适当的函数变换方法，再次获得几种精确解，从而新旧结果一起构成耦合标量场方程的8种精确解，其中有6种孤子解，另外两种为三角函数形式的周期解.讨论了这些结果在物理学其他几个著名方程上的应用. 关键词：     

EXACT SOLUTIONS TO LATTICE BOUSSINESQ-TYPE EQUATIONS

In this paper several kinds of exact solutions to lattice Boussinesq-type equations are constructed by means of generalized Cauchy matrix approach, including soliton solutions and mixed solutions. The introduction of the general condition equation set yields that all solutions contain two kinds of plane-wave factors.     

推广的B-BBM方程和B-BBM方程的显式精确解

研究了BBM方程和推广的B-BBM方程解之间的形变理论,通过给出的一类新的形变关系可从BBM方程的已知解形变出推广的B-BBM方程的显式精确解,并附有这种方法的应用举例.还对B-BBM方程运用齐次平衡法获得其解的显式表示 关键词： 形变理论 齐次平衡法 显式精确解 推广的B-BBM方程 B-BBM方程     

环形振子势的精确解

将环形振子势的Schrödinger方程在球坐标系中进行变量分离.然后求解了角向方程和径向方程,给出了精确的能谱方程.获得了用普遍的缔合Legendre多项式表示的归一化的角向波函数和用合流超几何函数表示的归一化的径向波函数.     

两个严格可解双原子分子势函数的散射态解与转动修正

文献［１］中提出了一个新的势函数，其Ｓｃｈｒｄｉｎｇｅｒ方程严格可解。同时提出一个新的变量变换关系，用超几何级数严格求解了双曲型ＰｓｃｈｌＴｅｌｅｒ分子势Ｓｃｈｒｄｉｎｇｅｒ方程的束缚态。文内进一步讨论这两个势函数Ｓｃｈｒｄｉｎｇｅｒ方程散射态的严格解，并求出了Ｓ波的散射相移。文献中关于修正ＰｓｃｈｌＴｅｌｅｒ势及无反射势散射态的结果均作为特例包含在这篇文章更一般的结论之中。此外还用一个简单的方法考虑了转动能修正，对ＨＦ基态转动谱作了具体计算     

爱因斯坦方程的一组严格的双孤立波解

由一个对角型的度规出发,给出了一组严格的引力双孤立波解。这组解是处处正则和稳定的,它们描写两个分别沿正z方向和负z方向的光速传播的孤立波,而且在彼此碰撞后不会改变自己形状并继续传播,文章最后还讨论了这组解相应的时空奇异性和能量正定性问题。 关键词：     

非线性耦合微分方程组的精确解析解

提出了利用耦合的Riccati方程组的某些特解构造非线性微分方程组精确解析解的一种方法.应用这种方法研究了两个耦合的常微分方程组,系统地获得了它们的一些精确解.给出了非线性浅水波近似方程组和非线性Schr?dinger-KdV方程组若干新的孤波解. 关键词： 非线性耦合方程组 Riccati方程组 符号计算 孤波     

Letter: A Cylindrically Symmetric Solution in Einstein-Maxwell-Dilaton Gravity

We consider the existence of Einstein-Maxwell-dilaton plus fluid systems for the case of stationary cylindrically symmetric spacetimes. An exact inhomogeneous -order solution is found, where the parameter parametrizes the non-minimally coupled electromagnetic field. Some its physical attributes are investigated and a connection with the already known Gödel-type solution is given. It is shown that our solution also survives in the string-inspired charged gravity framework. We find that a magnetic field has positive influence on the chronology violation unlike the dilaton influence.     

STATIC SPHERICALLY SYMMETRIC SOLUTION OF EINSTEIN GRAVITY COUPLED TO ELECTRO-MAGNETIC AND SCALAR FIELDS

The static spherically symmetric solution of Einstein gravity coupled to electromagnetic and scalar fields is obtained under the consideration of the self-gravitational interaction of the electromagnetic and scalar fields, which is singularity-free and stable.     

形式变量分离法及一般Hirota-Satsuma方程新的精确解

将形式变量分离方法推广应用于一个不可积的一般Hirota-Satsuma方程,得到了一些新的孤波解和周期波解. 关键词：     

SOME NEW AND EXACT EXPLICIT SOLUTIONS OF THE HIGHER ORDER BROER-KAUP EQUATIONS

A simple solitary wave solution and infinitely many rational function solutions, especially the closed form of the solution for the initial value problem of the higher order Broer-Kaup (BK) systems in (1+1) and (2+1) dimensions, are obtained by using the extended homogeneous balance method.     

Einstein场方程的一个平面对称非静态标量场解

求出一个特殊的标量场V=V(t-z)产生的平面对称度规的一个非静态解,并研究了它的对称性、奇异性等整体特性。 关键词：     

GROUP OF TRANSFORMATIONS WITH RESPECT TO THE COUNTERPART OF RAPIDITY AND RELATED FIELD EQUATIONS

The Lorentz-group of transformations usually consists of linear transformations of the coordinates, keeping as invariant the norm of the four-vector in (Minkowski) space-time. Besides those linear transformations, one may construct different forms of nonlinear transformations of the coordinates keeping unchanged that respective invariant. In this paper we explore nonlinear transformations of second-order which have a natural interpretation within the framework of Yamaleev's concept of the counterpart of rapidity (co-rapidity). The purpose of developed concept is to show that the formulae for energy and momentum of the relativistic particle become regular near the zero-mass and speed of light states. Furthermore, in a covariant formulation, the co-rapidity is presented as a four-vector which admits an extension of the Lorentz-group of transformations. In this paper we additionally show, that in the same way as the rapidity is related to the electromagnetic field, the co-rapidity is related to the field of strengths, which are given by a four-vector. The corresponding equations of such a field are also constructed.     

一类非线性耦合方程的孤子解

利用双参数假设给出了一类非线性耦合方程的若干孤子解公式,使物理上许多著名的方程作为该方程的特殊情形得到相应的孤子解,指正了一些文献的错误. 关键词： 非线性发展方程 双参数假设 孤子解     

广义经典力学系统的第一积分与变分方程特解的联系

给出了广义经典力学系统的变分方程,研究了变分方程的解与系统的第一积分之间的联系,并证明可由系统的第一积分求得变分方程的特解. 关键词： 广义经典力学系统 第一积分 变分方程     

Burgers方程新的精确解及初始值问题解的封闭形式

利用扩展齐次平衡法,求出了Burgers方程无穷多个单孤子解和无穷多个有理函数解,特别是得到了Hopf-Cole’s变换和方程初始值问题解的封闭形式.方法简单直接,并且可以推广到其它方程.     

利用CCD准确测量激光远场发散角

 利用CCD面阵接收器,通过标定的方法,将其准确安置在长焦距透镜后焦面上,并找出CCD 象元数与原场发散角的对应关系,从而迅速确定远场发散角。同时用短焦距透镜对 光束限制光阑成像,测得近场光斑光强分布。以激光束振幅函数的傅里叶变换作为理想衍射 极限,将远场发散角与之比较,可以得到用几倍衍射极限的方法表示的实际光束质量。     

A NEW PROCEDURE GENERATING THE SOLUTIONS OF STATIONARY AXIALLY SYMMETRIC GRAVITATIONAL FIELD EQUATIONS

A new procedure used to generate a set of solutions of stationary axially symmetric gravitational field equations is presented. It is shown that the Chandrasekhar metric is the most simple member of our solutions for n=1.Making use of this procedure we obtained a new exact solution of static axially sym-metric Einstein-Maxwell equations.It represents the exterior field of an isolated mass m with electrical dipolemoment.     

4D neutral signature VSI and CSI spaces

In this paper we present a number of four-dimensional neutral signature exact solutions for which the polynomial scalar curvature invariants all vanish (VSI spaces) or are all constant (CSI spaces), which are of relevance in current theoretical physics.     

原子与多模辐射场作用的动力学性质的精确求解

本文精确求解了一个二能级原子与一个多模辐射场相互作用的动力学问题．文中没有用到旋转波近似和偶极近似,而是运用相干态展开技术,求得了相互作用过程中原子的上下两能级的粒子数随时间的变化情况,并讨论了系统中光子数随频率的分布．计算机的模拟计算给出了一些有意义的结果．