摘要
Burgers方程在工程上有着重要的应用,它可以用来描述湍流、车队的交通流、氏族的随机迁移、化学工程中的分离等现象,对Burgers方程求解方法的研究有着重要的现实意义.对Burgers方程求解主要是应用差分和微分两方面的方法来展开求解的,1/G展开法是近年来发展起来的求解非线性偏微分方程的一种较为有效的微分解法.采用微分方程方面的方法,利用1/G展开法对一类Burgers方程进行求解,得到了此方程的一类孤立波解和扭曲波解,同时描绘出解的图像并分析解的结构和变化趋势.
Burgers equation has important applications in engineering,it can be used to describe the turbulence,the team of traffic flow,random migration of clan,the phenomenon such as separation in chemical engineering etc..It is of great practical significance to study the method of Burgers equation’s solution.Burgers equations are solved mainly by using the two aspects of difference and differential methods,The 1/G expansion method is developed in recent years to solve the nonlinear partial differential equations of a relatively effective differential method.In this paper we adopt the method of differential equation,and use the1/G expansion method to solve a class of Burgers equations,then we obtain a class of solitary wave solutions and distorted wave solutions.And we depict the image of the solution and analyze the structure and changing trend of the figure of the solution.
作者
陆求赐
张宋传
王学彬
LU Qiu-ci;ZHANG Song-chuan;WANG Xue-bin(School of Humanities and Teacher Education of Wuyi University,Wuyishan 354300,China;School of Mathematics and Computer Science of Wuyi University,Wuyishan 354300,China)
出处
《数学的实践与认识》
2021年第7期299-303,共5页
Mathematics in Practice and Theory
基金
福建省教育厅科技项目(JA15512,JAT160519)
福建省科技厅项目(2017J01769)
高级引进人才科研启动项目(YJ201802)。
关键词
BURGERS方程
1/G展开法
行波变换
孤立波解
扭曲波解
burgers equation
1/G expansion method
travel wave translation
solitary wave solution
distorted wave solutions
