一个3×3矩阵谱问题及其 Darboux 变换

华东师范大学学报(自然科学版) ›› 2007, Vol. 2007 ›› Issue (5): 54-61.

一个3×3矩阵谱问题及其 Darboux 变换

周甄川^1,2, 周振江^2,3

1. 黄山学院数学系, 安徽黄山 245041; 2. 华东师范大学计算机科学技术系, 上海 200062; 3. 南京人口管理干部学院信息科学系, 南京 210042

收稿日期:2006-06-21 修回日期:2006-10-09 出版日期:2007-09-25 发布日期:2007-09-25
通讯作者: 周甄川

3×3 Matrix Spectral Problem and Its Darboux Transformation(Chinese)

ZHOU Zhen-chuan ^1,2, ZHOU Zhen-jiang ^2,3

1. Department of Mathematics, Huangshan College, Huangshan Anhui 245041, China ; 2. Department of Computer Science and Technology, East China Normal University , Shanghai 200062, China ; 3. Department of Information Science, Nanjing College for Population Programme Management, Nanjing 210042, China

Received:2006-06-21 Revised:2006-10-09 Online:2007-09-25 Published:2007-09-25
Contact: ZHOU Zhen-chuan

摘要/Abstract

摘要： 构造了一个基于3×3 矩阵谱问题的 Lax 对, 求出了该 Lax 对所对应的梯队.
该梯队不仅包含了 KdV 和 mKdV 方程, 还包含了高阶 NLS 方程. 此外, 根据谱问题的规范变换, 导出了此谱问题的 Darboux 变换, 并得出了其精确解.

关键词: Lax对, 梯队, Darboux变换, 高阶 NLS 方程, Lax对, 梯队, Darboux变换, 高阶 NLS 方程

Abstract: The Lax pair of a 3×3 matrix spectral problem was
constructed and the hierarchy corresponding to this Lax pair was
also obtained. This hierarchy includes not only KdV and mKdV
equations but also high-order NLS equation. Besides, with the help
of the gauge transformation of spectral problem, the Darboux
transformation of this $3\times3$ matrix spectral problem was
deduced and its explicit solutions were given.

Key words: hierarchy, Darboux transformation, high-order NLS equation, Lax pair, hierarchy, Darboux transformation, high-order NLS equation

中图分类号:

TN915.04

周甄川;周振江;. 一个3×3矩阵谱问题及其 Darboux 变换[J]. 华东师范大学学报(自然科学版), 2007, 2007(5): 54-61.

ZHOU Zhen-chuan;ZHOU Zhen-jiang;. 3×3 Matrix Spectral Problem and Its Darboux Transformation(Chinese)[J]. Journal of East China Normal University(Natural Sc, 2007, 2007(5): 54-61.