|本期目录/Table of Contents|

Beta效应和耗散影响的广义变系数KdV方程及其孤立波解(PDF)

《内蒙古大学学报(自然科学版)》[ISSN:1000-9035/CN:22-1262/O4]

期数:
2019年06期
页码:
625-630
栏目:
研究论文
出版日期:
2019-11-15

文章信息/Info

Title:
Generalized Variable Coefficient KdV Equation with the Effect of Beta and Dissipation and Its Solutions
作者:
周兰锁吴国栋王海龙尹晓军
内蒙古农业大学理学院,呼和浩特 010018
Author(s):
ZHOU Lan-suoWU Guo-dongWANG Hai-longYIN Xiao-jun
College of Science,Inner Mongolia Agriculture University,Hohhot 010018,China
关键词:
广义变系数KdV方程 试探函数法 孤立波解
Keywords:
KdV equation with generalized variable coefficient trial function method solitary wave solution
分类号:
-
DOI:
-
文献标识码:
A
摘要:
采用含有beta效应和耗散项的正压无量纲准地转位涡方程来研究热带大气剪切流中的非线性Rossby波的振幅.首先通过约化摄动法,推导出用广义变系数KdV方程可以描述Rossby波的振幅变化属性的结论; 然后利用试探函数法,解出了广义变系数KdV方程在系数满足一定条件下的孤立波解,并且借助Matlab数学软件作图的辅助方式,对影响孤立波解的振幅、波宽和波速的因素做出了分析.结果显示,受广义变系数KdV方程中耗散项的影响Rossby波的振幅随时间以指数函数形式衰减.
Abstract:
The barotropic fluids dimensionless quasi-geostrophic potential vortex equation with beta effect and dissipative term is used to study the amplitude of nonlinear Rossby wave in tropical atmospheric shear flow.Firstly,the generalized variable coefficient KdV equation is derived by reduced perturbation method.It describes the amplitude variation property of the Rossby wave.Then,using the trial function method,the solitary wave solution of the generalized variable coefficient KdV equation is obtained,when the coefficients of the equation satisfy a certain conditions.Subsequently,graphics are described with help of Matlab software.The amplitude,wave width and wave velocity ofthe solitary wave solution are analyzed.The results show that the amplitude of the Rossby wave is attenuated exponentially with time by the dissipation term in the generalized variable coefficient KdV equation.

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备注/Memo

备注/Memo:
收稿日期:2019-05-31; 修回日期:2019-09-17
基金项目:国家自然科学基金(11762011); 内蒙古自治区高等学校科学研究项目(NJZY19045); 内蒙古自治区自然科学基金项目(2018MS01006); 内蒙古农业大学基础学科科研启动基金(JC2016001;JC2018003)
作者简介:周兰锁(1977-),男,内蒙古托克托县人,讲师,硕士.主要从事微分方程及动力系统研究.E-mail:zhoulansuo@126.com
通信作者:尹晓军(1982-),男,内蒙古乌兰察布人,讲师,博士.主要从事地球流体力学研究.E-mail:yinxiaojun_2002@163.com
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