{"title":"On the extended 2-dimensional Toda lattice models","authors":"Conghan Wang, Shangshuai Li, Da-jun Zhang","doi":"10.1134/S0040577924120043","DOIUrl":null,"url":null,"abstract":"<p> An extended <span>\\(2\\)</span>-dimensional Toda lattice equation is investigated by means of the Cauchy matrix approach. We introduce a direction parameter in the extension and represented the equation as a coupled system in a <span>\\(3\\)</span>-dimensional space. The equation can also be considered as a negative-order member in one direction of the discrete Kadomtsev–Petviashvili equation. By introducing the <span>\\(\\tau\\)</span>-function and an auxiliary direction, the equation can be bilinearized in a <span>\\(4\\)</span>-dimensional space with a single <span>\\(\\tau\\)</span>-function. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2049 - 2061"},"PeriodicalIF":1.0000,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S0040577924120043","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
An extended \(2\)-dimensional Toda lattice equation is investigated by means of the Cauchy matrix approach. We introduce a direction parameter in the extension and represented the equation as a coupled system in a \(3\)-dimensional space. The equation can also be considered as a negative-order member in one direction of the discrete Kadomtsev–Petviashvili equation. By introducing the \(\tau\)-function and an auxiliary direction, the equation can be bilinearized in a \(4\)-dimensional space with a single \(\tau\)-function.
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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