概率波和非概率波

对于把克莱因-戈尔登方程当作是玻色子的方程的看法提出异议,认为它是所有微观粒子均要满足的方程,但它却不能成为任何一类粒子的波动方程.提出了克-戈方程中包含着概率和非概率两类波的概念,认为概率波还要遵从一个对时和空都是一阶导数的方程,这才是粒子的波动方程.不同种类粒子性质的不同则体现在他们概率波类型的不同上.     

环形非球谐振子标量势与矢量势的Klein-Gordon和Dirac方程的束缚态

通过求解环形非球谐振子势的 Klein-Gordon 和 Dirac方程,给出了束缚态波函数与能量方程的精确解,并指出非相对论Schr?dinger方程与具有相等标量势和矢量势的Klein-Gordon 方程以及Dirac方程之间具有数学结构上的等价性。     

Identical motion in relativistic quantum and classical mechanics

The Klein-Gordon equation for the stationary state of a charged particle in a spherically symmetric scalar field is partitioned into a continuity equation and an equation similar to the Hamilton-Jacobi equation. There exists a class of potentials for which the Hamilton-Jacobi equation is exactly obtained and examples of these potentials are given. The partitionAnsatz is then applied to the Dirac equation, where an exact partition into a continuity equation and a Hamilton-Jacobi equation is obtained.     

The superposition method in seeking the solitary wave solutions to the KdV-Burgers equation

In this paper, starting from the careful analysis on the characteristics of the Burgers equation and the KdV equation as well as the KdV-Burgers equation, the superposition method is put forward for constructing the solitary wave solutions of the KdV-Burgers equation from those of the Burgers equation and the KdV equation. The solitary wave solutions for the KdV-Burgers equation are presented successfully by means of this method.     

Lie Symmetry Analysis,Conservation Laws and Exact Power Series Solutions for Time-Fractional Fordy-Gibbons Equation

In this paper, the time fractional Fordy-Gibbons equation is investigated with Riemann-Liouville derivative. The equation can be reduced to the Caudrey-Dodd-Gibbon equation, Savada-Kotera equation and the Kaup-Kupershmidt equation, etc. By means of the Lie group analysis method, the invariance properties and symmetry reductions of the equation are derived. Furthermore, by means of the power series theory, its exact power series solutions of the equation are also constructed. Finally, two kinds of conservation laws of the equation are well obtained with aid of the self-adjoint method.     

New Solitary Wave Solutions to the KdV-Burgers Equation

Based on the analysis on the features of the Burgers equation and KdV equation as well as KdV-Burgers equation, a superposition method is proposed to construct the solitary wave solutions of the KdV-Burgers equation from those of the Burgers equation and KdV equation, and then by using it we obtain many solitary wave solutions to the KdV-Burgers equation, some of which are new ones.PACS: 02.30.Jr; 03.65.Ge     

描述氨水体系VLE行为适宜热力学模型的研究

基于对氨／水体系气液平衡研究的文献调查,选择了Ｇｕｉｌｌｅｖｉｃ等提出的一套等温数据为工作基础,本文研究了状态方程法与活度系数法对氨／水体系气液平衡性质预测的适用性．其中状态方程法分别选用理想体系的计算方法、ＢＷＲ方程、ＳＲ－Ｐｏｌａｒ方程、ＬＫ－Ｐ方程和ＲＫＳ方程;活度系数法是基于气相选用ＲＫＳ方程,液相分别选用ＮＲＴＬ模型、电解质ＮＲＴＬ模型、ＵＮＩＱＵＡＣ模型、ＵＮＩＦＡＣ模型和Ｗｉｌｓｏｎ方程。本研究发现,活度系数法并没有良好表现,而 ＬＫ－Ｐ方程和 ＲＫＳ方程对氨／水体系气液平衡性质预测的适用性显然优于其它方法。     

二甲醚专用状态方程的研究

在对二甲醚实验数据进行文献调研的基础上,运用生物进化优化算法开发了二甲醚的饱和蒸汽压、饱和液密度及饱和汽密度方程和 Helmholtz 状态方程.其中二甲醚的饱和蒸汽压、饱和液密度和饱和汽密度方程的平均绝对偏差分别为 0.50%、0.38%和 0.55%.新的 Helmholtz 状态方程计算密度的偏差在液相区为 0.1%以内,临界点附近为 l%,可以很好地用于工程计算.     

Application of the complex point source method to the Schrödinger equation

The paraxial wave equation is a reduced form of the Helmholtz equation. Its solutions can be directly obtained from the solutions of the Helmholtz equation by using the method of complex point source. We applied the same logic to quantum mechanics, because the Schrödinger equation is parabolic in nature as the paraxial wave equation. We defined a differential equation, which is analogous to the Helmholtz equation for quantum mechanics and derived the solutions of the Schrödinger equation by taking into account the solutions of this equation with the method of complex point source. The method is applied to the problem of diffraction of matter waves by a shutter.     

An Invariance for (2+1)-Extension of Burgers Equation and Formulae to Obtain Solutions of KP Equation

In this article, we study the (2+1)-extension of Burgers equation and the KP equation. At first, based on a known Bäcklund transformation and corresponding Lax pair, an invariance which depends on two arbitrary functions for (2+1)-extension of Burgers equation is worked out. Given a known solution and using the invariance, we can find solutions of the (2+1)-extension of Burgers equation repeatedly. Secondly, we put forward an invariance of Burgers equation which cannot be directly obtained by constraining the invariance of the (2+1)-extension of Burgers equation. Furthermore, we reveal that the invariance for finding the solutions of Burgers equation can help us find the solutions of KP equation. At last, based on the invariance of Burgers equation, the corresponding recursion formulae for finding solutions of KP equation are digged out. As the application of our theory, some examples have been put forward in this article and some solutions of the (2+1)-extension of Burgers equation, Burgers equation and KP equation are obtained.     

Exact and explicit solitary wave solutions to some nonlinear equations

Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative Φ⁴-model equation, the generalized Fisher equation, and the elastic-medium wave equation.     

The electromagnetic coupling in Kemmer-Duffin-Petiau theory

We analyze the electromagnetic coupling in the Kemmer-Duffin-Petiau (KDP) equation. Since the KDP equation which describes spin-0 and spin-1 bosons is of Dirac type, we examine some analogies with and differences from the Dirac equation. The main difference with the Dirac equation is that the KDP equation contains redundant components. We will show that as a result certain interaction terms in the Hamilton form of the KDP equation do not have a physical meaning and will not affect the calculation of physical observables. We point out that a second order KDP equation derived by Kemmer as an analogy to the second order Dirac equation is of limited physical applicability as (i) it belongs to a class of second order equations which can be derived from the original KDP equation and (ii) it lacks a back-transformation which would allow one to obtain solutions of the KDP equation out of solutions of the second order equation.     

完整系统三阶Lagrange方程的一种推导与讨论

从牛顿运动方程出发，推导了完整系统关于广义加速度的Lagrange方程.讨论了该方程与传统分析力学中的Lagrange方程的相容性问题.结果显示，三阶Lagrange方程可以通过对Lagrange方程求一阶时间导数得到，表明它们是相容的.因此三阶Lagrange方程提供了一种不同于传统Lagrange方程方法的求解物体运动方程的途径. 关键词： Lagrange方程 加速度能量 广义坐标     

Direct linearization of nonlinear difference-difference equations

Starting from the linear integral equation for the solutions of the Korteweg-de Vries (KdV) equation, we obtain the direct linearization of a general nonlinear difference-difference equation. In a continuum limit this equation reduces to a general integrable differential-difference equation which contains e.g. the Toda equation and the discrete KdV and MKdV as special cases.     

Simple Soliton Solution Method for the Combined KdV and MKdV Equation

Malfliet first proposed a simple solution method for the multisoliton solutionofthe KdV equation. Abdel-Rahman used Malfliet's method in a slightly modifiedform, and gave the multisoliton solution of the mKdV equation, RLW equation,Boussinesq equation, and modified Boussinesq equation. In this paper, we solvethe soliton solution of the cKdV=nmKdV equation by using this method.     

Wave propagation in a random medium: The solution of the m-nth moment equation with different wavenumbers

The moment equation with different wavenumbers and different transverse coordinates for wave propagation in a random medium is a linear differential equation. It often appears in the study of problems related to wave propagation in a random medium. The differential equation can be converted into an integral equation by using Green's functions and the integral equation can be solved by iteration. The moment equation is solved by the method of successive scatters, too. The solution of the moment equation is a Dyson expansion. The physical implication of the successive solution of the moment equation with different wavenumbers is explained.     

不同势函数状态方程湿空气性质的模拟研究

本文从L-J维里状态方程、L-J径向状态方程,TIP4P维里状态方程以及TIP4P径向状态方程四种模型出发,利用分子动力学模拟技术,进行了湿空气性质的研究.对不同状态方程的模拟结果的稳定性进行了探讨,发现径向状态方程的稳定性要好于维里状态方程,最后采用径向分布方程及TIP4P模型,模拟了湿空气的性质,结果表明湿空气在低温、高压和高含湿量下,其性质不再接近于理想气体的性质.     

Three types of generalized Kadomtsev－Petviashvili equations arising from baroclinic potential vorticity equation

By means of the reductive perturbation method, three types of generalized (2+1)-dimensional Kadomtsev--Petviashvili (KP) equations are derived from the baroclinic potential vorticity (BPV) equation, including the modified KP (mKP) equation, standard KP equation and cylindrical KP (cKP) equation. Then some solutions of generalized cKP and KP equations with certain conditions are given directly and a relationship between the generalized mKP equation and the mKP equation is established by the symmetry group direct method proposed by Lou et al. From the relationship and the solutions of the mKP equation, some solutions of the generalized mKP equation can be obtained. Furthermore, some approximate solutions of the baroclinic potential vorticity equation are derived from three types of generalized KP equations.