完整Coriolis力作用下带有外源强迫的非线性KdV方程  

The Nonlinear KdV Equation Under External Forcing With the Complete Coriolis Force

作　　者：尹晓军[1,2] 杨联贵[1] 宋健[3] 张瑞岗[1] 杨红丽[1] 刘全生[1] YIN Xiao-jun YANG Lian-gui SONG Jian ZHANG Rui-gang YANG Hong-li LIU Quan-sheng(School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R. China College of Science, Inner Mongolia Agricultural University, Hohhot 010018, P.R.China College of Science, Inner Mongolia University of Technology, Hohhot 010051, P.R. China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]内蒙古农业大学理学院,呼和浩特010018 [3]内蒙古工业大学理学院,呼和浩特010051

出　　处：《应用数学和力学》2017年第9期1053-1060,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11362012);国家自然科学基金青年科学基金(11202092;11301592)~~

摘　　要：利用摄动方法,从描写既有Coriolis力垂直分量又含有水平分量的位涡方程出发,给出了近赤道非线性Rossby波所满足的具有外源强迫的非线性KdV方程,并利用Jacobi椭圆函数展开法,求解了改进后的非线性KdV方程的行波解及孤立波解.通过分析KdV方程的行波解,指出Coriolis力的水平分量和外源对Rossby波动的影响.The nonlinear KdV equation under external forcing was deduced from the potential vorticity equation involving both the vertical and the horizontal components of the Coriolis force with the perturbation method near the equatorial Rossby waves. Then the periodic solution of the model was obtained by means of the Jacobi elliptic functions. It is shown that the horizontal components of the Coriolis force play an important role in the structures of the Rossby waves.

关 键 词：完整Coriolis力 JACOBI椭圆函数 非线性ROSSBY波 

分 类 号：P401[天文地球—大气物理学与大气环境]