单胶子交换梯形近似下Bethe-Salpeter方程赝标解

将在动量空间具有积分形式的单胶子交换梯形近似下Bethe-Salpeter方程化为微分方程,求出该方程在四动量为零时的赝标解全部分量,其中第一分量为已知的Goldstein解.     

理想流体球的爱因斯坦场方程内部严格解研究

当静态的具有球对称性的理想流体的密度是径向坐标的函数时，Oppenheimer-Volkoff(OV) 方程成为Riccati方程-根据OV方程的一个已知特解，能将它变换成可积分的Bernoulli方程 ，严格地求得OV方程的通解和另一特解，进一步得到理想流体球的爱因斯坦场方程的内部严 格解，即度规分量的解析表示式- 关键词： 爱因斯坦场方程 OV方程 理想流体球内部严格解     

《广义相对论入门讲座》连载⑧——广义相对论的实验验证

1 史瓦西解史瓦西给出了爱因斯坦方程的一个严格解,这是一个静止、球对称星体外部的真空解,其中不为零的度规分量为     

环状非有心势场中Schr(o)dinger方程的精确解

提出了一个新的环状非有心势模型.利用Nikiforov-Uvarov方法求解了其满足的Schrodinger方程,得到了束缚态波函数的精确解及能谱方程.讨论了角向分量对径向分量的影响及相关参数取特定值时的特殊情况.     

环状非有心势场中Schrdinger方程的精确解

提出了一个新的环状非有心势模型.利用Nikiforov-Uvarov方法求解了其满足的Schrdinger方程,得到了束缚态波函数的精确解及能谱方程.讨论了角向分量对径向分量的影响及相关参数取特定值时的特殊情况。     

适用于射频加热的迴旋动力方程

参照Chen和Tsai的方法导出了在迴旋频率附近,以三个电场分量为独立场量的线性迴旋动力方程。它适用于研究非均匀等离子体中的射频加热。并给出了该方程在轴对称托卡马克装置中的解。     

非线性Schroedinger方程的包络形式解

扩展了最近提出的F展开方法以构造非线性演化方程更多的精确解，即将F展开法中的一阶非线性常微分方程和单变量的有限幂级数代之以类似的一阶常微分方程组和两个变量的有限幂级数，这两个变量是一阶常微分方程组的解分量．作为例子，用扩展的F展开法解非线性Schroedinger方程，得到了很丰富的包络形式的精确解，特别是以两个不同的Jacobi椭圆函数表示的解．显然，扩展的F展开方法也可以解其他类型的非线性演化方程．     

一维Morse势的Dirac方程的束缚态

在标量型和矢量型Morse势相等的条件下,给出了Dirac方程束缚态的一维二分量波函数和一维四分量波函数的精确解.并且在求精确解时,运用一种新的自变量变换方法,使方程求解变得比较简单.     

守恒无伪解麦克斯韦方程间断元研究:(Ⅰ)一维和二维情况

考察了电、磁场分量分别基于不同近似函数空间展开的一维和二维Maxwell方程间断元求解方法。结合中心数值通量和电、磁场分量近似函数空间的不同组合,构造了各种间断元算子。通过用这些算子在规则和不规则网格上编码分析一维和二维金属腔的谐振模式,详细考察了算子的收敛和伪解支持性,并据此对基函数进行了优选。算子在时域和频域对谐振模式的计算结果彼此符合良好。优选的Maxwell方程间断元算子不仅同时具备能量守恒和免于伪解的特性,且无需引入辅助变量,为设计高品质Maxwell方程间断元算法和研发相关电磁场模拟软件提供了支撑。     

用试探方程法求变系数非线性发展方程的精确解

将试探方程法应用到变系数非线性发展方程的精确解的求解.以两类变系数KdV方程为例，在相当一般的参数条件下求得了丰富的精确解，其中包括新解. 关键词： 试探方程法 变系数KdV方程 类椭圆正弦(余弦)波解 类孤子解     

一类Landau-Ginzburg-Higgs扰动方程孤子的近似解

利用解析方法研究了一类Landau-Ginzburg-Higgs方程. 由广义变分迭代理论得到了相应方程的解,从而得到了对应方程孤子的近似解. 关键词： 孤子 扰动 变分迭代     

Self-Consistent Sources Extensions of Modified Differential-Difference KP Equation

In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the mKP equation. It is also shown that the solution of the modified differential-difference KP equation is related to the solution of the differential-difference KP equation through a Miura transformation. We first present the Grammian solution to the modified differential-difference KP equation, and then produce a coupled modified differential-difference KP system by applying the source generation procedure. The explicit N-soliton solution of the resulting coupled modified differential-difference system is expressed in compact forms by using the Grammian determinant and Casorati determinant. We also construct and solve another form of the self-consistent sources extension of the modified differential-difference KP equation, which constitutes a Bäcklund transformation for the differential-difference KP equation with self-consistent sources.     

广义Landau-Ginzburg-Higgs方程孤子解的扰动理论

利用扰动方法研究了一类广义Landau-Ginzburg-Higgs方程.引入一个同伦映射，将原方程的解表示为渐近展开式，然后用相应的线性方程的解来近似地表示.讨论了方程的解与得到的近似解的关系. 关键词： 孤子 扰动 同伦映射     

A solution of radiative transfer in isotropic plane-parallel atmosphere by integrating Milne equation

In this paper we solve the inversion problem of the radiative transfer process in the isotropic plane-parallel atmosphere by iterative integrations of the Milne integral equation. As a result, we obtain the scattering function in the form of a cubic polynomial in optical thickness. The author has already solved the same problem by iterative integrations of Chandrasekhar's integral equation. In the Milne integral equation, both the cosines of the viewing angles and the optical thickness are integral variables, while in Chandrasekhar's integral equation the cosines of the viewing angles are variables but the optical thickness is not. We derive several series of exponential-like functions as intermediate derivations. Their convergences are evaluated by the author's previous work in the solution of Chandrasekhar's integral equation. The truncated scattering function up to the third order in optical thickness thus obtained is identical to that obtained from Chandrasekhar's integral equation, though their apparent forms are different. Chandrasekhar pointed out that the solution of Chandrasekhar's integral equation does not have a uniqueness of solution. The Milne equation, in contrast, has been proven to have a unique solution. We discuss the uniqueness of the solution by these two methods.     

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.     

一类非线性方程类孤波的近似解法

采用了一个简单而有效的技巧,研究了一类扰动发展方程.首先引入求解一个相应典型方程的类孤波近似解,然后利用泛函映射方法得到了原扰动发展方程的近似解,指出了近似解级数的收敛性,并用解析方法,讨论了近似解的精度.     

An Approach for Solving Short-Wave Models for Camassa-Holm Equation and Degasperis-Procesi Equation

In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. To solve the ordinary differential equation, we assume the soliton solution in the explicit expression and obtain the travelling wave solution. By the transformation back to the original independent variables, the soliton solution of the original partial differential equation is derived. We investigate the short wave model for the Camassa-Holm equation and the Degasperis-Procesi equation respectively. One-cusp soliton solution of the Camassa-Holm equation is obtained. One-loop soliton solution of the Degasperis-Procesi equation is also obtained, the approximation of which in a closed form can be obtained firstly by the Adomian decomposition method. The obtained results in a parametric form coincide perfectly with those given in the present reference. This illustrates the efficiency and reliability of our approach.     

一类广义非线性扰动色散方程孤立波的近似解

采用了一个简单而有效的技巧,研究了一类非线性扰动色散方程.首先引入求解相应典型方程的孤立波解.然后利用同伦映射方法得到了原非线性扰动色散方程奇异孤立波的近似解.     

The effect of the heat capacity of the liquid phase on the heat of fusion liquidus equation of compound semiconductors

We have critically examined the assumptions involved in the derivation of Vieland's widely used heat of fusion liquidus equation for binary compounds and conclude that the thermodynamic form of this equation ignores the relative partial molar heat capacity of the liquid solution. Taking into account this quantity, we obtain the generalized heat of fusion equation which is exact and show its complete equivalence to its alternative, the heat of formation equation. The generalized result provides a correction term to Vieland's equation which can be expressed as a function of the activity coefficients at the compound composition. Applying the correction term to the activity coefficients derived for a number of useful solution models, we find that the regular solution form of Vieland's equation is exact, as shown previously, if α (interchange energy) is a constant or a linear function of temperature. But when α is expanded as an nth order polynomial in temperature (simple solution), Vieland's equation is inexact for n ? 2. In addition, it is demonstrated that for a regular associated solution and for Darken's quadratic representation, Vieland's thermodynamic equation is exact only with certain restrictions, while for a quasi-chemical solution it is invalid.     

A fast method for the solution of the Helmholtz equation

In this paper, we consider the numerical solution of the Helmholtz equation, arising from the study of the wave equation in the frequency domain. The approach proposed here differs from those recently considered in the literature, in that it is based on a decomposition that is exact when considered analytically, so the only degradation in computational performance is due to discretization and roundoff errors. In particular, we make use of a multiplicative decomposition of the solution of the Helmholtz equation into an analytical plane wave and a multiplier, which is the solution of a complex-valued advection–diffusion–reaction equation. The use of fast multigrid methods for the solution of this equation is investigated. Numerical results show that this is an efficient solution algorithm for a reasonable range of frequencies.