Wm -algebras and fractional powers of difference operators

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-07-22 DOI:10.1088/1361-6544/ad5fd8

Gloria Marí Beffa

引用次数: 0

Abstract

In this paper we define a Poisson pencil associated to a lattice Wm-algebras defined in a recent paper by Izosimov and Marí Beffa (2023 Int. Math. Res. Not.2023 17021–59). We then prove that this Poisson pencil is equal to the one defined in 2013 by Marí Beffa and Wang (2013 Nonlinearity26 2515) and the author using a type of discrete Drinfel’d–Sokolov reduction. We then show that, much as in the continuous case, a family of Hamiltonians defined by fractional powers of difference operators commute with respect to both structures, defining the kernel of one of them and creating an integrable hierarchy in the Liouville sense.

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Wm 矩阵和差分算子的分数幂

在本文中，我们定义了与伊佐西莫夫和玛丽-贝法（2023 Int. Math. Res. Not.2023 17021-59）最近一篇论文中定义的晶格 Wm-gebras 相关的泊松铅笔。然后，我们利用一种离散的 Drinfel'd-Sokolov 还原法证明，这个泊松铅笔等于 Marí Beffa 和 Wang (2013 Nonlinearity26 2515) 以及作者在 2013 年定义的那个泊松铅笔。然后我们证明，与连续情况一样，由差分算子的分数幂定义的哈密顿族与这两种结构都相通，从而定义了其中一种结构的内核，并创建了柳维尔意义上的可积分层次结构。

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

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.