【摘要】 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解的方法。借助Cole-Hope变换,A=0且B=0为Af+B=0的解,获得了(2+1)维Burgers方程和Kdv方程的n-孤子解。这种方法可以求解一系列的偏微分方程。更多还原

【Abstract】 Differential equations contain linear and nonlinear differential equations. Research of the nonlinear differential equations are 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 of the original with linear partial differential equation approximation problem must also consider nonlinear effects. From the traditional point of view, the solutions of partial differential equation is very difficult. After several decades of research and exploration, we have found some tectonic solution method. In this paper, With the help of Cole-Hope transform, one of the conditions for the equation Af+B=0 to be true if A=0 and B=0, n-soliton solutions of(2+1) dimensional Burgers equation and Kdv equation have been presented. This method could solve a series of partial differential equations.更多还原