【摘要】 求非线性偏微分方程的精确解非常重要,Burgers方程是一个模拟冲击波的传播和反射的非线性偏微分方程,它在非线性偏微分方程中具有重要地位。给出了Burgers方程的全新的精确解,具体的方法如下:首先,对方程进行行波变换;然后,分别利用双曲函数法和改进的双曲函数法给定它不同形式的拟解,其中拟解的项数由齐次平衡法确定,拟解中的函数满足Riccati方程;再将拟解代入行波变换后的方程,得到一个方程组;最后,借助计算机代数系统Mathematica解此方程组,确定拟解,即为全新的精确解。这种方法求得的Burgers方程的精确解,包含了一些文献的结果,也修正了某些文献的结论。这种方法可以用来求一系列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.Burgers equation is a nonlinear partial differential equation for simulating the propagation and reflection of shock waves.Burgers equation plays an important role in nonlinear partial differential equations.A great amount of work has been done to obtain the exact solution of the Burgers equation.In this paper,we obtain new exact solution of the Burgers equation.Firstly,the traveling wave transformation of the Burgers equation is carried out;Secondly,Respectively by using hyperbolic function method and improved hyperbolic functions method,different forms of quasi solution was given,the number in the solution is determined by the homogeneous balance method,function with the Riccati equation;Finally,the quasi solution is determined by the computer algebra system Mathematica,which is a new exact solution.The exact solution not only contains the results of some literature,but also revises some of the conclusions of the literature.This method can be used to find a series of exact solutions of partial differential equations.更多还原