完整Coriolis力作用下带有外源强迫的非线性ZK方程  

Nonlinear ZK equation under the external forcing with a complete Coriolis force

作　　者：尹晓军[1,2] 杨联贵[1] 刘全生[1] 苏金梅[2] 吴国荣[2] YIN Xiao-jun;YANG Lian-gui;LIU Quan-sheng;SU Jin-mei;WU Guo-rong(School of Mathematical Science, Inner Mongolia University, Hohhot 010021, China;College of Science, Inner Mongolia Agriculture University, Hohhot 010018, China)

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

出　　处：《高校应用数学学报（A辑）》2017年第4期423-430,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

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);内蒙古农业大学基础科研启动基金(JC2016001)

摘　　要：在正压流体中,从包含完整Coriolis参数的准地转位涡方程出发,在弱非线性长波近似下,采用多时空尺度和摄动方法,推导出大气非线性Rossby波振幅演变满足带有外源强迫的二维Zakharov-Kuznetsov(ZK)方程.然后利用Jacobi椭圆函数展开法,求解了ZK方程的椭圆正弦波解和孤立波解.分析结果表明,Coriolis参数的水平分量将影响二维Rossby波传播的频率特征,而外源不仅对二维Rossby波动的传播的频率有影响,对振幅也产生一个调制作用.In this paper,the nonlinear two-dimensional Zakharov-Kuznetsov(ZK)equation under the external forcing in a potential vorticity equation which includes both the vertical and horizontal components of Coriolis parameter is derived by using multiscale and perturbation expation method in a weakly nonliear,long wave approximation near the equatorial Rossby waves.And then the periodic solution for the model is obtained with the help of Jacobi elliptic functions.It is show that the horizontal components of Coriolis parameter and external forcing play an important role in the structures of the Rossby waves.

关 键 词：科氏参数 JACOBI椭圆函数 ZK方程 

分 类 号：O175.14[理学—数学]