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

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

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摘要

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

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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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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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