1) variable coefficient equation
变系数方程
1.
Considering the(2+1) dimensional variable coefficient equation,doing some unknown functions transformation for seed solutions of the equation,we make full use of Backlund transformation and performing mathematical calculations to obtain a series of exact solutions,in which some solution contains arbitrary functions.
考虑一般的变系数方程,对方程的种子解作适当的未知函数变换,然后利用backlund变换通过演算获得(2+1)维变系数方程的一系列精确解,其中有的解中含有任意函数,当这些任意函数取某些特殊函数时,这些解具有丰富的结构。
2) Poisson equation with variable coefficient
变系数Poisson方程
1.
The key ingredient is that the solver of the governing equations is built based on a projection algorithm and a Poisson equation with variable coefficient for the hydrodynamic pressure is solved by using a multigrid technique.
应用高精度类谱紧致Padé格式,配合特征边界(NSCBC)技术,采用方程分裂的投射算法,并通过可变系数Poisson方程多重网格求解,使得散度约束条件获得满足,克服了模拟中虚假热膨胀问题,发展了针对低马赫数射流火焰的直接模拟程序。
3) Huxley equation with variable coefficients
变系数Huxley方程
1.
By using the homogeneous balance principle,an auto-Bcklund transformation (BT) to the Huxley equation with variable coefficients is derived.
用齐次平衡原则导出了一个变系数Huxley方程的自-Bcklund变换(BT),利用BT获得了变系数Huxley方程的若干精确解。
4) variable coefficient KdV equation
变系数KdV方程
1.
Exact solutions of the general variable coefficient KdV equation with external force term;
含外力项的广义变系数KdV方程的精确解
2.
By using a transformation,the variable coefficient KdV equation is reduced to a nonlinear ordinary differential equation(NLODE).
利用一种函数变换将变系数KdV方程约化为非线性常微分方程(NLODE),并由此NLODE出发获得变系数KdV方程的若干精确类孤子解。
3.
In this paper,by using of new special function transform in truncated expansion method,the three kinds of exact solutions of the general variable coefficient KdV equation are obtained.
文章在截断展开法中采用特殊的函数变换形式,从而求出了广义变系数KdV方程三类新的精确解。
5) differential equation with varied coefficient
变系数微分方程
1.
The differential equation with varied coefficient of the SH-wave in the functionally graded materials is established.
建立了功能梯度材料中SH波的变系数微分方程。
2.
The differential equation with varied coefficient of one-dimensional P wave in the functionally graded materials is established.
建立了功能梯度材料中一维 P 波的标准变系数微分方程,对材料的弹性模量和质量密度均呈指数函数变化情况进行了求解,弹性模量、质量密度相同分布时,给出子位移的解析解；弹性模量、质量密度不同分布时,给出了位移的 WKBJ 近似解析解。
补充资料：Poisson方程
Poisson方程
Poisson equation
氏汾佣方程【P川，，抑闪皿泳班;nyacc。湘yp翻“二~‘J 击署干反域内部的~一个质量分布产生的位势〔po-tential)所满足的偏微分方程.关于空问R”(性)3)的N台沱翔位势(NewtDn potential)与R，的对数位势(1o，rithmic Poteniial)，Po姚on方程具有如下形式 声日2“ 凸日=Zes，，-气，=一a吸舀，口砚X，.“.X_尹 ，二l口X了其中p=p(义，，…，x。)是这个质量分布的密度，a(Sn)二，:兀，:/，/f(n/2+一)是R”中单位球面S”的面积、而f(。/2+l)是r函数的值. Po讹on方程是非齐次椭圆型方程的一个基本例子.s.Po讹on(1812)首先研究这种方程.【补注】映射川，八(u)定义一个态射，它把上调和函数的局部差构成的层映人R”上的测度层.由此引导出在调和空间(11anllohic sPace)框架中Poisson问题的处理方法.见【Al].
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
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