含变系数或强迫项的KdV方程的新解

Jacobi椭圆函数展开法被推广并用于求解另一种形式的KdV方程的新的精确解,所求解的这类KdV方程包括一种典型的变系数的KdV方程和具有强迫项（随机项）的KdV方程．用这种方法得到的新的类周期解在极限条件下可以退化为类孤立波解或类冲击波解．     

Periodic Structure of Equatorial Envelope Rossby Wave Under Influence of Diabatic Heating

A simple shallow-water model with influence of diabatic heating on a β-plane is applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By the asymptotic method of multiple scales, the cubic nonlinear Schro^edinger (NLS for short) equation with an external heating source is derived for large amplitude equatorial envelope Rossby wave in a shear flow. And then various periodic structures for these equatorial envelope Rossby waves are obtained with the help of Jacob/elliptic functions and elliptic equation. It is shown that phase-locked diabatic heating plays an important role in periodic structures of rational form.     

Exact Periodic-Wave Solutions for （2＋1）-Dimensional Boussinesq Equation and（3＋1）-Dimensional KP Equation

The (2 1)-dimensional Boussinesq equation and (3 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained.     

直流圆形线圈径向磁感应强度研究

基于毕奥-萨伐尔定律，分别考虑及不考虑直流通电圆形线圈的径向宽度和纵向厚度，推导出两种情况下该线圈沿径向方向的磁感应强度分布公式.然后，利用Matlab软件对获得的分布公式进行数值积分，得到理论上的磁感应强度分布数据.为了考察理论值的正确性，通过设计自制圆形线圈，进行实际测量.结果表明，考虑径向宽度和纵向厚度的影响时，磁感应强度实际测量值与理论值的相对误差较小.通过理论计算与实验研究相结合考察直流通电圆形线圈沿径向方向的磁感应强度分布，既能消除电磁感应法测交变磁场实验中磁场分布的系统误差，还可加强学生对电磁理论的理解与认识，提高电磁学课程的教学效果.