Darboux变换的可逆性，可换性和周期性

本文讨论了R^1 n中的一类可积系统的Darboux变换的可逆性，得出可逆的充要条件，并利用这条件制作出具体的可逆的Darboux变换。利用可逆性的研究和Darboux变换的可换性定理，得出了2N（N≥2），为周期的闭的Darboux变换序列的存在性。

On the Invertibility, Permutability and Periodicity of Darboux Transformations

It has been shown that the Darboux transformation method is valid for some integrable systems in the space-time R~(n 1). The theorem of permutability holds as well. In the present paper a necessary and sufficient condition is fond under which the inverse of a Darboux transformation is also a Darboux transformation. A kind of invertible Darboux transformation is constructed explicitly. Based on the theorem of permutability and the theorem on the existence of the invertible Darboux transformations the existence of closed sequences of Darboux transformations of period 2N is determined, where N is any positive integer.