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1·In the chapter 2, we find the separation of variables solutions for nonlinear reaction diffusion equation (2.4) by utilizing the group foliation method.

在第二章中我们主要利用群分支法来求解非线性扩散方程(2.4)的分离变量解。

2·We derive the analytic solution of the non-homogeneous fractional diffusion-wave equation under the mixed boundary conditions using the method of separation of variables.

利用分离变量方法导出了在混合边界条件下的非齐次分数阶扩散-波动方程的解析解。

3·By using separation of variables and double Fourier series, we obtain a solution to the initial-boundary value problem of the forced vibration of this rectangular membrane.

利用分离变量法和二重傅里叶级数的方法，得到了矩形膜的受迫振动初边值问题的解。

4·The Schrdinger equation is given directly from the classical Hamiltonian function of a damping harmonic oscillator, and its solution is obtained by the separation of variables.

写出阻尼谐振子的哈密顿函数，对其直接量子化，用分离变量法得出了薛定谔方程的解。

5·Separation of variables is employed to solve the differential equation under the boundary condition of two ends of the girder being simply supported, and the solution of stress is…

在两端简支的边界条件下采用分离变量法求解偏微分方程，得到用级数表示的应力解，然后根据剪力滞系数的定义即可得到组合箱梁翼板的剪力滞系数。

6·Secondly, the method of separation of variables and the eigensolution expansion method are used to obtain the analytical solutions of thick plates under corresponding boundary conditions.

然后，采用分离变量法和特征函数展开法在相应的边界条件下求出级数解。

7·Firstly, the expressions of free vibration of moderately thick plates in polar coordinates are derived and the general solutions are obtained by the means of method of separation of variables.

首先，导出了用极坐标系描述的中厚板自由振动板的微分方程，用分离变量法求得其一般解。

8·The Green's functions for electric and magnetic vector potentials in a sectoral wave guide and its cavity are derivated by using the separation of variables, Fourier transform and residue theory.

文中介绍了扇面直波导及其腔体中电矢量位和磁矢量位的格林函数，采用分离变量法、傅里叶变换法和留数定理导出了格林函数的具体表达式。

9·The temperature field around a straight buried pipe was analyzed using conformal mapping, separation of variables and boundary discretization. A series solution was obtained for the temperature field.

为了对直埋管道保温层及其土壤邻域的温度场进行较精确的分析，采用保形映射、分离变量和边界离散法对地下直埋管道的温度场进行分析，得到了级数形式的解。

10·By using variables separation in the complex number field, the real analytical solution in the form of Fourier series was obtained.

在复数域内利用分离变量法，得到了这类方程的级数形式的解析解，而最后的解是实数形式。