On integrability of the deformed Ruijsenaars-Schneider system

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.4213/rm10105e

Anton Vladimirovich Zabrodin

引用次数: 1

Abstract

We find integrals of motion for the recently introduced deformed Ruijsenaars-Schneider many-body system, which is the dynamical system for poles of elliptic solutions to the Toda lattice with constraint of type B. Our method is based on the fact that the equations of motion for this system coincide with those for pairs of Ruijsenaars-Schneider particles which stick together preserving a special fixed distance between the particles. We also obtain Bäcklund transformations and integrable time discretization of the deformed Ruijsenaars-Schneider system, which is shown to be the dynamical system for poles of elliptic solutions to the fully discrete Kadomtsev-Petviashvili equation of type B. In additon, we propose a field analogue of the deformed Ruijsenaars-Schneider system on a space-time lattice. Bibliography: 35 titles.

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变形rujsenaars - schneider系统的可积性

我们求出了最近引入的变形的rujsenaars - schneider多体系统的运动积分，该系统是具有b型约束的Toda晶格椭圆解的极点的动力系统。我们的方法是基于这样一个事实，即该系统的运动方程与保持粒子间特殊固定距离的rujsenaars - schneider粒子对的运动方程相一致。我们还得到了变形的Ruijsenaars-Schneider系统的Bäcklund变换和可积时间离散化，该系统被证明是b型完全离散Kadomtsev-Petviashvili方程椭圆解极点的动力系统。此外，我们提出了变形的Ruijsenaars-Schneider系统在时空格上的场模拟。参考书目:35种。

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

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.