{"title":"Higher Symmetries of Lattices in 3D","authors":"Ismagil T. Habibullin, Aigul R. Khakimova","doi":"10.1134/S1560354724060017","DOIUrl":null,"url":null,"abstract":"<div><p>It is known that there is a duality between the Davey – Stewartson type coupled systems and a class of integrable two-dimensional Toda type lattices. More precisely, the coupled systems are generalized symmetries for the lattices and the lattices can be interpreted as dressing chains for the systems. In our recent study we have found a novel lattice which is apparently not related to the known ones by Miura type transformation. In this article we describe higher symmetries to this lattice and derive a new coupled system of DS type.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 6","pages":"853 - 865"},"PeriodicalIF":0.8000,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S1560354724060017","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
It is known that there is a duality between the Davey – Stewartson type coupled systems and a class of integrable two-dimensional Toda type lattices. More precisely, the coupled systems are generalized symmetries for the lattices and the lattices can be interpreted as dressing chains for the systems. In our recent study we have found a novel lattice which is apparently not related to the known ones by Miura type transformation. In this article we describe higher symmetries to this lattice and derive a new coupled system of DS type.
期刊介绍：
Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.
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