{"title":"The Lax pairs and conserved quantities of the delay Lotka-Volterra equation","authors":"Hiroshi Matsuoka, Kenta Nakata, Ken-ichi Maruno","doi":"arxiv-2402.02204","DOIUrl":null,"url":null,"abstract":"The delay Lotka-Volterra equation is a delay-differential extension of the\nwell known Lotka-Volterra equation, and is known to have N-soliton solutions.\nIn this paper, Backlund transformations, Lax pairs and infinite conserved\nquantities of the delay Lotka-Volterra equation and its discrete analogue are\nconstructed. The conserved quantities of the delay Lotka-Volterra equation turn\nout to be complicated and described by using the time-ordered product of linear\noperators.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"254 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Exactly Solvable and Integrable Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2402.02204","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
The delay Lotka-Volterra equation is a delay-differential extension of the
well known Lotka-Volterra equation, and is known to have N-soliton solutions.
In this paper, Backlund transformations, Lax pairs and infinite conserved
quantities of the delay Lotka-Volterra equation and its discrete analogue are
constructed. The conserved quantities of the delay Lotka-Volterra equation turn
out to be complicated and described by using the time-ordered product of linear
operators.
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