N-Dimensional Lattice Integrable Systems and Their bi-Hamiltonian Structure on the Time Scale Using the R-Matrix Approach

被引：0

作者：

Fang, Yong ^{[1
]}

Sang, Xue ^{[1
]}

Yuen, Manwai ^{[2
]}

Zhang, Yong ^{[1
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

[2] Educ Univ Hong Kong, Dept Math & Informat Technol, 10 Lo Ping Rd, Hong Kong, Peoples R China

来源：

AXIOMS | 2024年 / 13卷 / 03期

基金：

中国国家自然科学基金;

关键词：

N-dimensional lattice integrable systems; time scale; R-matrix approach; bi-Hamiltonian structure; DISPERSIONLESS SYSTEMS; ALGEBRA; CONSTRUCTION; SYMMETRIES; OPERATORS; EQUATIONS; FIELD;

D O I：

10.3390/axioms13030136

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A time scale is a special measure chain that can unify continuous and discrete spaces, enabling the construction of integrable equations. In this paper, with the Lax operator generated by the displacement operator, N-dimensional lattice integrable systems on the time scale are given by the R-matrix approach. The recursion operators of the lattice systems are derived on the time scale. Finally, two integrable hierarchies of the discrete chain with a bi-Hamiltonian structure are obtained. In particular, we give the structure of two-field and four-field systems.

引用

页数：16

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