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: 10.3969/j.issn.1005-3085.2022.04.015

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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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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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