Backlund变换理论发展简述及其新方法

本文首先简要介绍Bcklund变换理论的发展过程,然后介绍一种寻找微分方程Bcklund变换的新方法——wahlquist-Estabrook过程。该方法是目前处理微分方程Bcklund问题的最有效方法.尽管该方法在理论上可应用于任意维数的偏微分方程组,但是实际上它所能处理的主要是二维问题。例如,在应用该方法处理完整Navicr-Stokcs方程(四维问题)时,所得到的是无意义结果.但是,在应用该方法处理定常二维Navicr-Stokcs方程时,确实可以得到正常的Bcklund映射,以及Bcklund变换. 

BACKLUND TRANSFORMATIONS AND ITS NEW METHOD

In this paper, first we briefly survey the evolution of the theory of Backlund transformation, then a new method for seeking Backlund transformations for differential equations, the Wahlquist-Estabrook procedure, is outlined. This method is the most effective approach to date for treating Backlund problem of differential equations. Although it is theoretically applicable to systems of partial differential equations with any dimensions, this method is actually limited for problems which are mainly two-dimens...