利用Riccati方程求解Burgers方程  

Solving Burgers Equation Using Riccati Equations

作　　者：林府标 LIN Fu-biao(School of Mathematics and Economics, Guizhou University of Finance and Economics, Guiyang 550025, Chin)

机构地区：[1]贵州财经大学数统学院,贵州贵阳550025

出　　处：《数学的实践与认识》2017年第21期260-264,共5页Mathematics in Practice and Theory

基　　金：2017年度贵州财经大学引进人才科研项目

摘　　要：应用李群理论中的伸缩变换群,把非线性二阶偏微分方程-Burgers方程转化为非线性非齐次一阶常微分方程-Riccati方程,将Riccati方程转化为Bernoulli方程和齐次线性二阶常微分方程,从而找到了Riccati方程的许多解,最后进一步求出了Burgers方程许多新的解析解.In relevant reference by applying scaling group of Lie group theory, the second- order nonlinear partial differential equation-Burgers equation is reduced to nonhomogeneous first-order nonlinear ordinary differential equation-Riccati equation. However, in this paper, Riccati equation is converted into Bernoulli equation and homogeneous second-order linear ordinary differential equation, which leads to many solutions of Riccati equation are found, finally a lot of new solutions of Burgers equation are presented.

关 键 词：Riccati方程 BERNOULLI方程 齐次线性二阶常微分方程 非线性二阶偏微分方程 BURGERS方程 精确解 

分 类 号：O175.2[理学—数学]