{"title":"Ideals Generated by Differential Equations","authors":"O. Kaptsov, Олег Викторович Капцов","doi":"10.17516/1997-1397-2020-13-2-170-186","DOIUrl":null,"url":null,"abstract":"Abstract. We propose a new algebraic approach to study compatibility of partial differential equations. The approach uses concepts from commutative algebra, algebraic geometry and Gröbner bases to clarify crucial notions concerning compatibility such as passivity and reducibility. One obtains sufficient conditions for a differential system to be passive and proves that such systems generate manifolds in the jet space. Some examples of constructions of passive systems associated with the sinh-Cordon equation are given.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Siberian Federal University. Mathematics and Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17516/1997-1397-2020-13-2-170-186","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract. We propose a new algebraic approach to study compatibility of partial differential equations. The approach uses concepts from commutative algebra, algebraic geometry and Gröbner bases to clarify crucial notions concerning compatibility such as passivity and reducibility. One obtains sufficient conditions for a differential system to be passive and proves that such systems generate manifolds in the jet space. Some examples of constructions of passive systems associated with the sinh-Cordon equation are given.
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
