Analytic Solution for Magnetohydrodynamic Stagnation Point Flow towards a Stretching Sheet

A steady two-dimensional magnetohydrodynamic stagnation point flow towards a stretching sheet with variable surface temperature is investigated. The analytic solution is obtained by homotopy analysis method. The convergence region is computed and the feature of the solution is discussed.     

一类非线性偏微分方程组的解析解

首先,利用共轭算子的性质,将张鸿庆等提出的求伴随算子对的方法推广到了求一类非线性(即部分非线性的)算子矩阵的伴随算子向量．其次,利用机械化的构造方法给出了求解一类非线性(即,部分非线性的,且以所有线性的为其特例)非齐次微分方程组的统一理论,即通过齐次化和三角化求得恰当的变换,从而将原方程组化为较简单的形式,一般为对角化的．最后利用该方法求得了一些弹性力学方程组的解析解．     

Analytic solutions of a class of nonlinear partial differential equations

An approach is presented for computing the adjoint operator vector of a class of nonlinear （that is, partial-nonlinear） operator matrices by using the properties of conjugate operators to generalize a previous method proposed by the author. A unified theory is then given to solve a class of nonlinear （partial-nonlinear and including all linear） and non-homogeneous differential equations with a mathematical mechanization method. In other words, a transformation is constructed by homogenization and triangulation, which reduces the original system to a simpler diagonal system. Applications are given to solve some elasticity equations.     

New Solitary Solutions of （2＋1）-Dimensional Variable Coefficient Nonlinear Schrodinger Equation with an External Potential

By a series of transformations, the （2＋1）-dimensional variable coefficient nonlinear Schr？dinger equation can turn to the Klein-Gordon equation. Many new double travelling wave solutions of the Klein-Gordon equation are obtained. Thus, the new solitary solutions of the variable coefficient nonlinear Schr？inger equation with an external potential can be found.     

微分方程一般解的任意性及其应用

首先基于形式理论,提出了计算对合微分方程双变元Hilbert多项式的算法.其次,通过考察微分表示,给出了计算微分方程一般解任意性的方法.最后结合张鸿庆提出的数学机械化中的＂AC=BD＂模式,给出了将超定方程组化为恰定方程的构造方法.     

Hyperelliptic Function Solutions of Three Genus for KP Equation Using Direct Method

In this paper, we will use a simple and direct method to obtain some particular solutions of （2＋1）- dimensional and （3＋ 1）-dimensional KP equation expressed in terms of the Kleinian hyperelliptic functions for a given curve y^2 = f（x） whose genus is three. We observe that this method generalizes the auxiliary method, and can obtain the hyperelliptic functions solutions.     

CDG方程和耦合KdV-MKdV方程的微分不变量

本文利用了Olver提出的等价活动标架方法,通过构造合适的活动标架,得到了CDG方程和耦合KdV-MKdV方程的微分不变量,并推得了微分不变量代数.     

变力的两种平均力

在物理过程中,常遇到变力作用的过程,涉及到平均力及有关问题计算．如：ＦΔｔ＝ｍｖ－ｍｖ０．及Ｆｓ＝Ｗ中平均力Ｆ是否为同一概念,下面从一道题的解答谈起：ＯＭＡ如图所示：弹簧振子在水平方向上作简谐振动,小球的质量为０．２５ｋｇ,弹簧的劲度系数为１００Ｎ／ｍ,振幅为０．２ｍ．求：①小球在平衡位置速度大小;②从最大位移到平衡位置弹力对小球做的功（忽略摩擦及弹簧质量）．解法１,从最大位移到平衡位置弹力对小球做的功Ｗ＝Ｆｓ＝１２ｋＡ·Ａ＝１２×１００×（０．２）２＝２Ｊ由动能定理Ｗ＝１２ｍｖ２ｖ＝２Ｗｍ＝…     

2-齐次多项式集合的吴消元法

1引言 考虑2-齐次多项式集合p,两组变量分别记为x=(x_1…,x_n)与y=(y_1…,y_m),p的零点集Zero(P)为有限点集.利用吴消无法([7],[6])可以将此类多项式集合完全三角化从而求得全部解,但这样消元的复杂度甚高.