Please wait a minute...
高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (4): 423-430    DOI:
    
Nonlinear ZK equation under the external forcing with a complete Coriolis force#br#
YIN Xiao-jun1;2, YANG Lian-gui1, LIU Quan-sheng1, SU Jin-mei2, WU Guo-rong2
1.School of Mathematical Science, Inner Mongolia University, Hohhot 010021, China;
2.College of Science, Inner Mongolia Agriculture University, Hohhot 010018, China
Download:   PDF(0KB)
Export: BibTeX | EndNote (RIS)      

Abstract  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.

Key words： complete parameter      Jacobi elliptic functions      Zakharov-Kuznetsov equation     
Received: 08 December 2016      Published: 01 December 2018
CLC:  O175.14  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
YIN Xiao-jun
YANG Lian-gui
LIU Quan-sheng
SU Jin-mei
WU Guo-rong
Cite this article:

YIN Xiao-jun, YANG Lian-gui, LIU Quan-sheng, SU Jin-mei, WU Guo-rong. Nonlinear ZK equation under the external forcing with a complete Coriolis force#br#. Applied Mathematics A Journal of Chinese Universities, 2017, 32(4): 423-430.

URL:

http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2017/V32/I4/423


完整Coriolis力作用下带有外源强迫的非线性ZK方程

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.

关键词： 科氏参数,  Jacobi椭圆函数,  ZK方程 
[1] ZHANG Shen-gui. Infinitely many periodic solutions for a class of Kirchhoff-type p(t)-Laplacian systems[J]. Applied Mathematics A Journal of Chinese Universities, 2018, 33(2): 223-331.
[2] Taogetusang. The new complexion solutions of the (2+1) dimension modified Zakharov-Kuznetsov equation [J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(1): 33-40.
[3] BAO Li-ping. A class of boundary value problem of singular perturbed semi-linear differential systems with discontinuous source term[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(4): 413-422.
[4] YUAN Rong, LIU Hui-fang. Complex oscillation of solutions of some second order non-homogeneous linear di?erential equations#br#[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(4): 431-436.
[5] LIU Jiang, ZHANG Long, JIANG Zhong-chuan, LI Yan-qing. Synchronous control on inverter system of grid connected high-power wind generators with nonlinear and pulse disturbance#br#[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(4): 388-402.
[6] HAN Jian-bang, SHEN Qi-xia. Double boundary layers of quadratic nonlinear singularly perturbed boundary value problem with infinite boundary values[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(3): 316-326.
[7] ZHANG Jian-song, ZHANG Yue-zhi, ZHU Jiang, YANG Dan-ping. Split characteristic mixed finite element methods for advection-dominated diffusion equation[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(3): 338-350.
[8] ZHANG Shen-gui, LIU Hua. Multiplicity of solutions for Kirchhoff type equation involving the $p$-Laplacian-like operator[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(2): 153-160.
[9] GE Zhi-xin, CHEN Xian-jiang, HOU Wei-gen. A forced vibration resonance phenomena with fractional derivative damping[J]. Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 410-416.
[10] LU Liang, GUO Xiu-feng. Existence of solutions for a nonlocal boundary value problem of fractional differential equations with $p$-Laplacian operator[J]. Applied Mathematics A Journal of Chinese Universities, 2015, 30(3): 262-270.
[11] HE Ze-rong, WU Peng, ZHOU Juan. Optimal harvesting of a discrete size-structured model constrained by ecological balance[J]. Applied Mathematics A Journal of Chinese Universities, 2015, 30(2): 171-179.
[12] CHEN Wen, YAO Jing-sun, SUN Guo-zheng. A nonlinear mixed boundary value problem for singularly perturbed differential equation[J]. Applied Mathematics A Journal of Chinese Universities, 2015, 30(1): 117-126.