| 一类广义NLS-MKdV方程族及其双哈密顿结构北大核心CSCD |
| |
| 引用本文： | 董凤娇,胡贝贝.一类广义NLS-MKdV方程族及其双哈密顿结构北大核心CSCD[J].工程数学学报,2022,39(4):672-680. |
| |
| 作者姓名： | 董凤娇 胡贝贝 |
| |
| 作者单位： | 1. 滁州学院计算机与信息工程学院，滁州 2390002. 滁州学院数学与金融学院，滁州 239000 |
| |
| 基金项目： | 国家自然科学基金 (12147115)；中国博士后科学基金 (2022M712833)；安徽省自然科学基金 (2108085QA09)；安徽省高校自然科学研究项目 (KJ2021A1094; KJ2021B03). |
| |
| 摘 要： | 从矩阵谱问题出发,讨论了一类广义NLS-MKdV方程族和双哈密顿结构。首先,基于Loop Lie代数sl (2, R)构造了的广义NLS-MKdV方程族。其次,利用迹恒等式(变分恒等式)得到了广义NLS-MKdV方程的双Hamilton结构表示形式。再者,构造了带自相容源的广义NLS-MKdV方程族。最后,借助Riccati方程研究了广义NLSMKdV方程族的守恒律。
|
| 关 键 词： | Lie代数 广义NLS-MKdV方程族 哈密顿结构 自相容源 守恒律 |
A Classical Generalized NLS-MKdV Hierarchy and Its Bi-Hamiltonian Structure with Self-consistent Sources |
| |
| DONG Fengjiao,HU Beibei.A Classical Generalized NLS-MKdV Hierarchy and Its Bi-Hamiltonian Structure with Self-consistent Sources[J].Chinese Journal of Engineering Mathematics,2022,39(4):672-680. |
| |
| Authors: | DONG Fengjiao HU Beibei |
| |
| Affiliation: | 1. School of Computer and Information Engineering, Chuzhou University, Chuzhou 239000
;
2. School of Mathematics and Finance, Chuzhou University, Chuzhou 239000; |
| |
| Abstract: | Starting from the matrix spectral problem, a class of generalized NLS-MKdV hierarchy and bi-Hamiltonian structures are discussed. Firstly, a generalized NLS-MKdV hierarchy is constructed based on the Loop Lie algebra sl $(2,{\bf R})$. Secondly, the bi-Hamilton structure representation of the generalized NLS-MKdV hierarchy is obtained by using the trace identity or variational identity. Furthermore, a class of generalized NLS-MKdV hierarchy with self-consistent sources is constructed. Finally, the conservation laws of the generalized NLS-MKdV hierarchy are studied by means of the Riccati equation. |
| |
| Keywords: | Lie algebra generalized NLS-MKdV hierarchy Hamiltonian structure self-consistent sources conservation laws |
| 本文献已被 维普 等数据库收录！ |
| 点击此处可从《工程数学学报》浏览原始摘要信息 |
|
点击此处可从《工程数学学报》下载全文 |
