Burgers方程的广义精确解

Generalized exact solutions of Burgers equation

为了解决Burgers方程的精确解,本文沿用将Burgers方程转化Riccati方程求其精确解的方法,利用Riccati方程不变量的关系,给出Riccati方程精确解的解形式,并且将原文Burgers方程转化为特殊的Riccati方程,推广到一般形式的Riccati方程,给出Burgers方程的广义精确解.结果表明Burgers方程的广义精确解将进一步扩大其方程的应用范围.

In order to solve the exact solution of Burgers equation,this paper uses the method of transforming Burgers equation into Riccati equation to find its exact solution,uses the relationship between the invariants of Riccati equation,gives the solution form of the exact solution of Riccati equation,and transforms the original Burgers equation into a special Riccati equation,which is extended to the general Riccati equation.The generalized exact solution of Burgers equation is given.The results show that the generalized exact solution of Burgers equation will further expand the application range of Burgers equation.