完整Coriolis力作用下的Boussinesq方程及其孤立波解

Boussinesq Equation and Its Solitary Wave Solution under Complete Coriolis Force

从含有完整Coriolis力作用下的正压准地转位涡方程出发研究热带气候剪切流中的非线性Rossby波的振幅。首先,利用坐标伸缩变换法、摄动展开法,推导出Rossby波的振幅满足带有强迫项的Boussinesq方程;然后借助于Jacobi椭圆函数展开法,获得了Boussinesq方程的行波解以及类孤立波解;最后,应用Matlab数学软件,获得了孤立波解三维图形以及平面图形。从图形结果显示可以得出孤立波的振幅随各物理参数的变化规律。

Based on the barotropic quasi geostrophic potential vorticity equation with complete Coriolis force,the amplitude of nonlinear Rossby waves in tropical climate shear flow is studied.Firstly,the amplitude of Rossby wave is derived to satisfy the nonlinear Boussinesq equation by using the coordinate expansion method and perturbation expansion method;Then the travelling wave solutions and solitary wave solutions of the nonlinear Boussinesq equation are obtained by means of Jacobi elliptic function expansion method;Finally,three-dimensional and plane figures of solitary wave solutions are obtained by using Matlab software.The results show that the amplitude of solitary wave varies with the physical parameters.