【摘要】 求非线性偏微分方程的精确解是非常重要的.为了获得它的精确解研究人员做了大量的工作.本文获得了Burgers方程和Boussinesq方程组的全新的精确解.具体的方法如下:首先对方程进行行波变换得到新方程,之后给定它的拟解,将拟解代入新方程,而得到一个方程组,借助计算机代数系统Mathematica解此方程组,以确定拟解,即为全新的精确解.这种方法求得Burgers方程和Boussinesq方程组的精确解,包含了某些文献的结果,也修正了某些文献的结论.这种方法可以求一系列的偏微分方程的精确解.更多还原

【Abstract】 It is very important to find the exact solution of nonlinear partial differential equations. A great deal of work has been done to obtain its exact solutions. In this paper,we obtain new exact solutions of Burgers equation and Boussinesq equations. The specific method is as follows: first,the traveling wave transformation of the equation is carried out to obtain the new equation,and then given its quasi solution,the quasi solution is substituted into the new equation,and a set of equations is obtained,with the help of the computer algebra system Mathematica,this set of equations is solved to determine the quasi-solution,that is,the new exact solution. This method was used to obtain the exact solutions of Burgers equation and Boussinesq equations,including the results of some literature as well as the conclusions of some literature. This method can be used to find exact solutions of a series of partial differential equations.更多还原