摘要
求非线性偏微分方程的精确解是非常重要的。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。为了获得它的精确解,首先对方程进行行波变换,之后分别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方程或给出函数的直接形式,后将拟解代入行波变换后的方程,从而得到一个方程组,借助计算机代数系统解此方程组,以确定拟解,即为全新的精确解。这种方法求得的(2+1)维Burgers方程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,还可以求一系列的偏微分方程的精确解。
It is very important to find the exact solution of nonlinear partial differential equations.Burgers equation was 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.To obtain the exact solution of the Burgers equation,firstly,the traveling wave transformation of(2+1)—dimensional Burgers equation was carried out.Secondly,different forms of quasi solution were given,the number in the solution was determined by the homogeneous balance method and the function in the quasi-solution satisfied the Riccati equation or was given the direct form of the function,Finally,the quasi solution was determined by the computer algebra system,which was a new exact solution.The exact solution not only contains the results of some literature,but also revised some of the conclusions of the literature.This method can be used to find a series of exact solutions of partial differential equations.
作者
李伟
LI Wei(College of Mathematical,Bohai University,Jinzhou 121013,China)
出处
《重庆理工大学学报（自然科学）》
CAS
北大核心
2019年第11期211-213,共3页
Journal of Chongqing University of Technology：Natural Science
基金
国家自然科学基金资助项目(11547005)
