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  

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

作　　者：陈利国[1,2] 杨联贵 CHEN Liguo;YANG Liangui(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,P.R.China;School of Statistics and Mathematics,Inner Mongolia University of Finance and Economics,Hohhot 010070,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]内蒙古财经大学统计与数学学院,呼和浩特010070

出　　处：《应用数学和力学》2020年第1期98-106,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11762011);内蒙古自然科学基金(2017MS0108)~~

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.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 generalizedβeffect,the shear basic flow,the external source and the dissipation are ex tremely important factors influencing the nonlinear Rossby wave.

关 键 词：BOUSSINESQ方程 非线性ROSSBY波 JACOBI椭圆函数 外源 耗散 

分 类 号：O29[理学—应用数学] P433[理学—数学]