Approximation Of The Direct Reduction Method Disturbance Burgers Equation

we often encounter many problems which can be abstracted into partial differential equations In real life.These partial differential equations can be divided into two patrs:one is linear problems,another is nonlinear problems. With the progressive development of science, the linear problem has been developed comprehensively. Therefore, the problems of nonlinear partial differential equations become the focus of many scientists.Among these problems,there is such a kind of nonlinear equations with an infinitesimal parameter is called nonlinear perturbed equation by us.Today,such equations have become the main object of research to scientists.However,what is the most concerned about by us is how to solve the problems of perturbed equation.The appearance of perturbation theorem provides a good tool for solving nonlinear perturbed equations.Fushchich and Shtelen established a new kind of method to sove the perturbed equation,called approximate symmetry perturbation method,according to bombine the symmetry reduction method with the perturbation theory. However,this method just can solve part of the nonlinear perturbed equqtions well.The scientists get the enlightenment from the approximate symmetry perturbation method and build a new method,called the approximate direct reduction method.This method which will be used in this article is combined with the perturbation theory and Clarkson and Kruskal's direct reduction method.This article will use the approximate direct reduction method to discusse the perturbed burgers equation with third dispersion and second dispersion.According to the perturbation theory,we can get a series solution of the perturbed equation.Through this series solution,we will get more simplified partial differential equations.Using the ratios of coefficients of every different derivatives have to be functions of z only,the original differential equation can be constantly reduced.Finally,the problem of the perturbed equations will be solved.