广义变系数mKdV方程及其孤立波解  

GENERALIZED VARIABLE COEFFICIENT MKDV EQUATION ANDITS SOLITARY WAVE SOLUTION

作　　者：栾金凤 LUAN jinfeng(Inner Mongolia Vocational College of Physical Education,Hohhot 010051,China)

机构地区：[1]内蒙古体育职业学院,呼和浩特010051

出　　处：《内蒙古农业大学学报（自然科学版）》2020年第4期84-89,共6页Journal of Inner Mongolia Agricultural University(Natural Science Edition)

基　　金：项目教学法在高职院校统计课程教学中的实践探究(NTZY2019012);数学课堂教学的思政教育探索(NTZY2019009)。

摘　　要：首先应用约化摄动展开法对含有Beta效应、耗散和外源的无量纲准地转位涡方程进行研究,得出大气运动中的Rossby波的振幅满足广义变系数mKdV方程的结论,分析出耗散仅对广义变系数mKdV方程色散项的系数产生影响,Beta效应会对广义变系数mKdV方程各项均有影响;其次应用试探函数法对所得的方程求得了孤立波解,分析了影响孤立波解的振幅、波宽和波速影响因素.The reduced perturbation expansion method was used to study the dimensionless quasi-geostrophic potential vorticity equation with Beta effect,dissipation and external sources.Results indicatedthat the amplitude of Rossby wave satisfied the generalized variable coefficient mKdV equation in atmospheric motion.The dissipation only affected the coefficients of the dispersion term of the generalized variable coefficient mKdV equation,and the Beta effecthad an influence on each term of thegeneralized variable coefficient mKdVequation.Then,the solitary wave solutionwas obtained through the trial function method,and the factors affecting the amplitude,wave width and wave velocity of the solitary wave solution wereanalyzed.

关 键 词：ROSSBY波 广义变系数mKdV方程 孤立波解 

分 类 号：P401[天文地球—大气物理学与大气环境]