一类Burgers方程的精确解

Exact solutions of a class of Burgers equations

微分方程包含线性和非线性微分方程。微分方程研究的主体是非线性微分方程,特别是非线性偏微分方程。很多意义重大的自然科学和工程技术问题都可归结为非线性偏微分方程的研究。另外,随着研究的深入,有些原来可用线性偏微分方程近似处理的问题,也必须考虑非线性的影响。从传统的观点来看,求偏微分方程的精确解是十分困难的。经过几十年的研究和探索,人们已经找到了一些构造精确解的方法。借助于Cole-Hope变换,积分变换法和拟解的方法,获得Burgers方程,(2+1)维Burgers方程,(2+1)维高阶Burgers方程的新的精确解。这种方法可以解决一系列的偏微分方程。

Differential equations contain linear and nonlinear differential equations.Research of the nonlinear differential equations is the subject of differential equations,especially nonlinear partial differential equations.Many significant natural science and engineering problems can be attributed to nonlinear partial differential equation.In addition,With the development of research,some problems that may be treated with originally linear partial differential equation approximation problem must also consider nonlinear effects.From the traditional point of view,the exact solutions of partial differential equation is very difficult.After several decades of research and exploration,researchers have found some tectonic exact solution method.In this paper,with the help of Cole-Hope transform,integral method and quasi solution method,some new exact solutions of Burgers equation,（2＋1）dimensional Burger equation and（2＋1）dimensional higher-order Burgers equation were presented.This method could solve a series of partial differential equations.