推广的β平面近似下带有外源和耗散强迫的非线性Boussinesq方程及其孤立波解

陈利国; 杨联贵

doi:10.21656/1000-0887.400067

推广的β平面近似下带有外源和耗散强迫的非线性Boussinesq方程及其孤立波解

doi: 10.21656/1000-0887.400067

陈利国^1,2,
杨联贵¹

¹内蒙古大学数学科学学院, 呼和浩特 010021;²内蒙古财经大学统计与数学学院, 呼和浩特 010070

基金项目: 国家自然科学基金(11762011);内蒙古自然科学基金(2017MS0108)

详细信息

作者简介:
陈利国（1976—)，男，副教授，博士生(E-mail: chenliguo66@163.com)；杨联贵（1961—），男，教授，博士，博士生导师(通讯作者. E-mail: lgyang@imu.edu.cn).

中图分类号: O29|P433|O175.2
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出版历程
- 收稿日期: 2019-02-27
- 修回日期: 2019-03-14
- 刊出日期: 2020-01-01

A Nonlinear Boussinesq Equation With External Source and Dissipation Forcing Under Generalized β Plane Approximation and Its Solitary Wave Solutions

CHEN Liguo^1,2,
YANG Liangui¹

¹School of Mathematical Sciences, Inner Mongolia University,Hohhot 010021, P.R.China;²School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, P.R.China

Funds: The National Natural Science Foundation of China(11762011)

摘要

摘要: 在推广的β平面近似下,从包含耗散和外源的准地转位涡方程出发,利用GardnerMorikawa变换和弱非线性摄动展开法,推导出带有外源和耗散强迫的非线性Boussinesq方程去刻画非线性Rossby波振幅的演变和发展.利用修正的Jacobi椭圆函数展开法,得到Boussinesq方程的周期波解和孤立波解,从解的结构分析了推广的β效应、切变基本流、外源和耗散是影响非线性Rossby波的重要因素.
- Boussinesq方程 /
- 非线性Rossby波 /
- Jacobi椭圆函数 /
- 外源 /
- 耗散
Abstract: Under generalized β plane approximation, based on the quasigeostrophic potential vorticity equation, and by means of the Gardner-Morikawa transform and the weak nonlinear perturbation expansion method, a Boussinesq equation with external source and dissipation forcing was derived to describe the generation and evolution of the Rossby wave amplitude. The periodic wave solutions and solitary wave solutions for the Boussinesq equation were presented with the modified Jacobi elliptic function expansion method. The solution structure shows that, the generalized β effect, the shear basic flow, the external source and the dissipation are extremely important factors influencing the nonlinear Rossby wave.
- Boussinesq equation /
- nonlinear Rossby wave /
- Jacobi elliptic function /
- external source /
- dissipation

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参考文献(34)

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推广的β平面近似下带有外源和耗散强迫的非线性Boussinesq方程及其孤立波解

doi: 10.21656/1000-0887.400067

作者简介:
陈利国（1976—)，男，副教授，博士生(E-mail: chenliguo66@163.com)；杨联贵（1961—），男，教授，博士，博士生导师(通讯作者. E-mail: lgyang@imu.edu.cn).

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A Nonlinear Boussinesq Equation With External Source and Dissipation Forcing Under Generalized β Plane Approximation and Its Solitary Wave Solutions

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留言板

推广的β平面近似下带有外源和耗散强迫的非线性Boussinesq方程及其孤立波解

doi: 10.21656/1000-0887.400067

作者简介: 陈利国（1976—)，男，副教授，博士生(E-mail: chenliguo66@163.com)；杨联贵（1961—），男，教授，博士，博士生导师(通讯作者. E-mail: lgyang@imu.edu.cn).

计量

出版历程

A Nonlinear Boussinesq Equation With External Source and Dissipation Forcing Under Generalized β Plane Approximation and Its Solitary Wave Solutions

计量

出版历程

目录

作者简介:
陈利国（1976—)，男，副教授，博士生(E-mail: chenliguo66@163.com)；杨联贵（1961—），男，教授，博士，博士生导师(通讯作者. E-mail: lgyang@imu.edu.cn).