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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-21 DOI:10.3390/axioms13030136

Yong Fang, Xue Sang, Manwai Yuen, Yong Zhang

引用次数: 0

Abstract

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.

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使用 R 矩阵方法研究 N 维晶格可积分系统及其时间尺度上的双哈密顿结构

时间尺度是一种特殊的度量链，可以统一连续空间和离散空间，从而构建可积分方程。本文利用位移算子产生的拉克斯算子，通过 R 矩阵方法给出了时间尺度上的 N 维网格可积分系统。网格系统的递归算子在时间尺度上得到了推导。最后，我们得到了具有双哈密尔顿结构的离散链的两个可积分层次。我们特别给出了两场和四场系统的结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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