{"title":"Wm -algebras and fractional powers of difference operators","authors":"Gloria Marí Beffa","doi":"10.1088/1361-6544/ad5fd8","DOIUrl":null,"url":null,"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.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"28 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinearity","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1088/1361-6544/ad5fd8","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
