{"title":"Polynomial dynamical systems associated with the KdV hierarchy","authors":"V.M. Buchstaber, E. Yu. Bunkova","doi":"10.1016/j.padiff.2024.100928","DOIUrl":null,"url":null,"abstract":"<div><div>In 1974, S.P. Novikov introduced the stationary <span><math><mi>n</mi></math></span>-equations of the Korteweg–de Vries hierarchy, namely the <span><math><mi>n</mi></math></span>-Novikov equations. These are associated with integrable polynomial dynamical systems, with polynomial <span><math><mrow><mn>2</mn><mi>n</mi></mrow></math></span> integrals, in <span><math><msup><mrow><mi>ℂ</mi></mrow><mrow><mn>3</mn><mi>n</mi></mrow></msup></math></span>. In this paper, we construct an infinite-dimensional polynomial dynamical system that is universal for all dynamical systems corresponding to the <span><math><mi>n</mi></math></span>-Novikov equations. Thus, we solve the well-known problem of the relationship between the <span><math><mi>n</mi></math></span>-Novikov equations for different <span><math><mi>n</mi></math></span>.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100928"},"PeriodicalIF":0.0000,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Partial Differential Equations in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666818124003140","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
In 1974, S.P. Novikov introduced the stationary -equations of the Korteweg–de Vries hierarchy, namely the -Novikov equations. These are associated with integrable polynomial dynamical systems, with polynomial integrals, in . In this paper, we construct an infinite-dimensional polynomial dynamical system that is universal for all dynamical systems corresponding to the -Novikov equations. Thus, we solve the well-known problem of the relationship between the -Novikov equations for different .