孤子族的生成及换位表示的一般结构

GENERATION OF SOLITON HIERARCHY AND GENERAL STRUCTURE OF ITS COMMUTATOR REPRESENTATONS

本文通过对谱问题的直接研究，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．

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.