Kaup-Newell矩阵谱问题及其相应的方程

Matrix Spectral Problem of Kaup-Newell and the Associated Soliton Equation Hierarchy

在从矩阵谱问题出发来构建孤立子发展方程及方程族是孤立子与可积系统理论的重要组成部分.首先介绍了从孤立子谱问题出发,得到相应的孤立子发展方程的多种方法;其次,以其中某种方法为例,通过考虑Kaup-Newell矩阵谱问题的广义形式,得到可积耦合的KaupNewell方程族.

It＇s an important part in soliton equations and integrable systems theory to build the soliton e- volution equations and hierarchies starting from the matrix speetral problem. Some general matrix spectral prob- lems were introduced, which were used to obtain soliton evolution equations. One way for example was chosen by considering the general form of Kaup - Newell matrix spectral problem to get eoupling Kaup - Newell hierarchies.