分离圆柱面与偏心圆柱面静电场问题的镜象解

基于静电场的叠加原理和唯一性定理,用镜象法求解由两圆柱导体所组成的分离圆柱面与偏心圆柱面静电场边值问题,推导出分离圆柱面与偏心圆柱面静电场边值问题的解析解。     

具有n维氢原子型标量势与矢量势的Klein-Gordon方程的束缚态

研究了具有n维氢原子型标量势和矢量势的Klein-Gordon方程的束缚态性质，获得了束 缚态的精确解-给出了精确的能谱方程和归一化的解析波函数，推导出径向平均值的两个递 推关系和部分低幂次径向平均值的解析表达式- 关键词： n维氢原子势 Klein-Gordon方程 束缚态 精确解     

求解线电荷与导体圆柱形成电场的新方法

用保角变换方法,将导体圆柱外区域映射为单位圆内区域,线电荷位置映射为单位圆圆心,从而直接写出导体圆柱外电势,并对结果进行详细讨论,还利用软件画出等势线簇图形.     

有弱偏置磁场及含时激光场中的非线性Gross-Pitaevskii方程新的精确解

利用映射方法和一个适当的变换，得到大量的有弱偏置磁场及含时激光场中的非线性Gross-Pitaevskii方程的新解，这些解包括椭圆函数解，椭圆函数叠加解，三角函数解，亮孤子解，暗孤子解和类孤子解。     

辅助方程构造带强迫项变系数组合KdV方程的精确解

在辅助方程法的基础上给出第一种椭圆辅助方程和函数变换相结合的一种方法,并借助符号计算系统Mathematica构造了带强迫项变系数组合KdV方程的类Jacobi椭圆函数精确解以及退化后的类孤子解和三角函数解. 关键词： 辅助方程 函数变换 变系数组合KdV方程 精确解     

二端面转轴相对转动非线性动力学系统的稳定性与近似解

建立了二端面转轴相对转动系统的非线性动力学方程.对于等力矩的动力学方程进行了定性分析，得到了方程的稳定性等性质.用平均方法求得方程在一定条件下的近似解. 关键词： 非线性动力学方程 稳定性 极限环 近似解     

扩展的Jacobi椭圆函数展开法和Zakharov方程组的新的精确周期解

对Jacobi椭圆函数展开法进行了扩展，且利用这一方法求出了Zakharov方程组的一系列新的精确周期解，在极限情况下可得到相应的孤波解，补充了前面研究的结果. 关键词： Jacobi椭圆函数展开法 非线性发展方程 精确解 周期解     

Analytical solution for spatially axisymmetric problem of thick-walled cylinder subjected to different linearly varying pressures along the axis and uniform pressures at two ends

To our best knowledge, in the open literature, there is no analytical solution of thick-walled cylinder subjected to uniform pressures at two ends and different inner-and outer-surface pressures that are constant circumferentially but vary linearly at different rates along the axis. We now present such a solution. After repeated trials, we have finally succeeded in finding a necessary new displacement function. Based on A. E. H. Love method, the stress, displacement and volume strain formulas are derived by using the new displacement function. The present results include the Lamé’s formulas as special cases. Furthermore, the results obtained here can be applied to not only the thick-walled cylinders subjected to uniform pressures on the inner and outer surface of the thick-walled cylinder, respectively, but also the cylinders subjected to uniform pressures at two ends and different inner-and outer-surface pressures that are constant circumferentially but vary linearly at different rates along the axis, respectively. Finally we give a numerical example to compare our exact method with the approximate method.     

The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term

By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of Korteweg--de Vries (KdV) equations with variable coefficients and a KdV equation with a forcible term are constructed with the help of symbolic computation system Mathematica, where the new solutions are also constructed.