{"title":"Symmetries of Toda type 3D lattices","authors":"I. T. Habibullin, A. R. Khakimova","doi":"arxiv-2409.07017","DOIUrl":null,"url":null,"abstract":"The duality between a class of the Davey-Stewartson type coupled systems and\na class of two-dimensional Toda type lattices is discussed. For the recently\nfound integrable lattice the hierarchy of symmetries is described. Second and\nthird order symmetries are presented in explicit form. Corresponding coupled\nsystems are given. An original method for constructing exact solutions to\ncoupled systems is suggested based on the Darboux integrable reductions of the\ndressing chains. Some new solutions for coupled systems related to the Volterra\nlattice are presented as illustrative examples.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","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-2409.07017","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 duality between a class of the Davey-Stewartson type coupled systems and
a class of two-dimensional Toda type lattices is discussed. For the recently
found integrable lattice the hierarchy of symmetries is described. Second and
third order symmetries are presented in explicit form. Corresponding coupled
systems are given. An original method for constructing exact solutions to
coupled systems is suggested based on the Darboux integrable reductions of the
dressing chains. Some new solutions for coupled systems related to the Volterra
lattice are presented as illustrative examples.
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