| 一个3×3矩阵谱问题及其 Darboux 变换 |
| |
| 引用本文： | 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. |
| |
| 作者姓名： | 周甄川 周振江 |
| |
| 作者单位： | [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 |
| |
| 基金项目： | 国家自然科学基金（110371044） |
| |
| 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 |
| 文章编号： | 1000-5641（2007）05-0054-08 |
| 收稿时间： | 2006-6-21 |
| 修稿时间： | 2006-06 |
3×3 Matrix Spectral Problem and Its Darboux Transformation |
| |
| ZHOU Zhen-chuan,ZHOU Zhen-jiang.3×3 Matrix Spectral Problem and Its Darboux Transformation[J].Journal of East China Normal University(Natural Science),2007,2007(5):54-61. |
| |
| Authors: | ZHOU Zhen-chuan ZHOU Zhen-jiang |
| |
| Institution: | 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 |
| |
| 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. |
| |
| Keywords: | Lax pair hierarchy Darboux transformation high-order NLS equation |
| 本文献已被 维普 等数据库收录！ |
| 点击此处可从《华东师范大学学报(自然科学版)》浏览原始摘要信息 |
| 点击此处可从《华东师范大学学报(自然科学版)》下载免费的PDF全文 |
