利用Riccati方程求解Burgers方程

Solving Burgers Equation Using Riccati Equations

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.