孤子族的生成及换位表示的一般结构

本文通过对谱问题ψｘ＝Ｕ（ｕ，λ）ψ的直接研究，利用谱梯度提供一条获得孤子方程族的途径，进一步，我们给出了孤子方程换位表示的一般结构，同时我们还将看到同一个谱问题可产生两族不同的孤子发展方程。

GENERATION OF SOLITON HIERARCHY AND GENERAL STRUCTURE OF ITS COMMUTATOR REPRESENTATONS

In this paper, through some direct studies of the spectral problem an approach for obtaining the hierarchy of soliton equations is presented by the use of spectral gradient. Moreover, a general structure of commutator representations for the soliton hierarchy is constructed. Meanwhile, it is revealed that the same spectral problem can produce two different hierarchies of soliton evolution equations.