Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1
Chinese Journal of Engineering Mathematics

Chinese Journal of Engineering Mathematics >

2022 , Vol. 39 >Issue 4: 672 - 680

DOI: https://doi.org/10.3969/j.issn.1005-3085.2022.04.015

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

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  • 1. School of Computer and Information Engineering, Chuzhou University, Chuzhou 239000
    2. School of Mathematics and Finance, Chuzhou University, Chuzhou 239000

Online 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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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

Cite this article

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 . DOI: 10.3969/j.issn.1005-3085.2022.04.015

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