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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (4): 672-680.doi: 10.3969/j.issn.1005-3085.2022.04.015

• • 上一篇    

一类广义 NLS-MKdV 方程族及其双哈密顿结构

董凤娇1,   胡贝贝2   

  1. 1. 滁州学院计算机与信息工程学院，滁州 239000
    2. 滁州学院数学与金融学院，滁州 239000
  • 出版日期:2022-08-15 发布日期:2022-10-15
  • 基金资助:
    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).

A Classical Generalized NLS-MKdV Hierarchy and Its Bi-Hamiltonian Structure with Self-consistent Sources

DONG Fengjiao1,   HU Beibei2   

  1. 1. School of Computer and Information Engineering, Chuzhou University, Chuzhou 239000
    2. School of Mathematics and Finance, Chuzhou University, Chuzhou 239000
  • Online:2022-08-15 Published:2022-10-15
  • Supported by:
    The National Natural Science Foundation of China (12147115); the Project funded by China Postdoctoral Science Foundation (2022M712833); the Natural Science Foundation of Anhui Province (2108085QA09); the University Natural Science Research Project of Anhui Province (KJ2021A1094; KJ2021B003).

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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 $(2,{\bf R})$ 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 NLS-MKdV 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

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.

Key words: Lie algebra, generalized NLS-MKdV hierarchy, Hamiltonian structure, self-consistent sources, conservation laws

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