尹晓军, 杨联贵, 刘全生, 张瑞岗. 非线性(2+1)维Zakharov-Kuznetsov方程及其孤立波解[J]. 云南大学学报(自然科学版), 2018, 40(4): 619-624. doi: 10.7540/j.ynu.20160719
引用本文: 尹晓军, 杨联贵, 刘全生, 张瑞岗. 非线性(2+1)维Zakharov-Kuznetsov方程及其孤立波解[J]. 云南大学学报(自然科学版), 2018, 40(4): 619-624. doi: 10.7540/j.ynu.20160719
YIN Xiao-jun, YANG Lian-gui, LIU Quan-sheng, ZHANG Rui-guang. The nonlinear(2+1) dimensional Zakharov-Kuznetsov equation and its solitary solution[J]. Journal of Yunnan University: Natural Sciences Edition, 2018, 40(4): 619-624. DOI: 10.7540/j.ynu.20160719
Citation: YIN Xiao-jun, YANG Lian-gui, LIU Quan-sheng, ZHANG Rui-guang. The nonlinear(2+1) dimensional Zakharov-Kuznetsov equation and its solitary solution[J]. Journal of Yunnan University: Natural Sciences Edition, 2018, 40(4): 619-624. DOI: 10.7540/j.ynu.20160719

非线性(2+1)维Zakharov-Kuznetsov方程及其孤立波解

The nonlinear(2+1) dimensional Zakharov-Kuznetsov equation and its solitary solution

  • 摘要: 在正压流体中,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,推导了近赤道非线性Rossby波振幅的演变所满足的非线性(2+1)维Zakharov-Kuznetsov(ZK)方程,并利用Jacobi椭圆函数展开法,求解了非线性Zakharov-Kuznetsov(ZK)方程的行波解及孤立波解.通过分析其方程的行波解及孤立波,表明Coriolis力的水平分量及β效应对Rossby波动产生一定的影响.

     

    Abstract: In barotropic fluids,based on the quasi-geostrophic barotropic vorticity equation which includes both the vertical and horizontal components of Coriolis force,we derive the nonlinear (2+1)dimensional Zakharov-Kuznetsov(ZK) quation by the perturbation method near the equatorial Rossby waves.And then the solitary waves solution for the ZK equation is obtained with the help of Jacobi elliptic functions.The results reveal the horizontal components of Coriolis force and the beta effect play an important role in the structures of the Rossby waves.

     

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