正压流体中具有beta效应的非线性Boussinesq方程及其多孤子解  

Nonlinear Boussinesq Equation with Beta Effect and Its Multi-soliton Solutions in Barotropic Fluid

作　　者：贺艳飞[1] 尹晓军[1] HE Yanfei;YIN Xiaojun(College of Sciences,Inner Mongolia Agricultural University,Hohhot 010018,China)

机构地区：[1]内蒙古农业大学理学院,呼和浩特010018

出　　处：《内蒙古大学学报（自然科学版）》2024年第2期132-137,共6页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金项目(12362037);内蒙古自然科学青年基金项目(2022QN01003);内蒙古高校青年科技英才项目(NJYT23099);内蒙古高校创新团队项目(NMGIRT2208);内蒙古高等学校科学研究项目(NJZY23114);内蒙古农业大学青年教师提升项目(BR220126)。

摘　　要：本文主要考虑了具有beta效应的大尺度Rossby波控制方程的多孤子解。首先,从传统意义下的正压准地转位涡方程出发,利用多尺度分析法、坐标变换法、泰勒展开法以及分离变量法,推导出大尺度Rossby波的振幅满足带有beta效应的非线性Boussinesq方程。然后,基于这个方程通过适当的变量代换给出了模型方程的Hirota双形式,并利用Hirota双线性方法获得了非线性Boussinesq方程的1-孤子解、2-孤子解、3-孤子解及N-孤子解。基于模型方程得到推广的beta效应能诱导生成Rossby波,并分析孤子解的结果表明,随着非线性系数的增大,孤子解的振幅在逐渐变小。The multi-soliton solutions of the governing equations of large scale Rossby waves with beta effect are considered.Firstly,starting from the traditional barotropic quasi-geostrophic potential vorticity equation,the amplitude of large-scale Rossby waves satisfies the nonlinear Boussinesq equation with beta effect by using multi-scale analysis,coordinate transformation method,taylor expansion method and separation of variables method.Then,based on this equation,the bilinear form of the equation is given through appropriate variable substitution,and 1-soliton solution,2-soliton solution,3-soliton solution and N-soliton solution of the nonlinear Boussinesq equation are obtained by using Hirota bilinear method.Based on the model equation,the generalized beta effect can induce the generation of Rossby waves.And the results show that the amplitude of soliton solution decreases with the increase of nonlinear coefficient.

关 键 词：BOUSSINESQ方程 ROSSBY波 HIROTA方法 多孤子解 

分 类 号：O29[理学—应用数学] P401[理学—数学] O351.2[天文地球—大气物理学与大气环境]