{"title":"On B-type family of Dubrovin–Frobenius manifolds and their integrable systems","authors":"Alexey Basalaev","doi":"10.1007/s11005-024-01867-z","DOIUrl":null,"url":null,"abstract":"<div><p>According to Zuo and an unpublished work of Bertola, there is a two-index series of Dubrovin–Frobenius manifold structures associated to a B-type Coxeter group. We study the relations between these structures for the different values of these indices. We show that part of the data of such Dubrovin–Frobenius manifold indexed by (<i>k</i>, <i>l</i>) can be recovered by the <span>\\((k+r,l+r)\\)</span> Dubrovin–Frobenius manifold.Continuing the program of Basalaev et al. (J Phys A: Math Theor 54:115201, 2021) we associate an infinite system of commuting PDEs to these Dubrovin–Frobenius manifolds and show that these PDEs extend the dispersionless BKP hierarchy.\n</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-024-01867-z","RegionNum":3,"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
According to Zuo and an unpublished work of Bertola, there is a two-index series of Dubrovin–Frobenius manifold structures associated to a B-type Coxeter group. We study the relations between these structures for the different values of these indices. We show that part of the data of such Dubrovin–Frobenius manifold indexed by (k, l) can be recovered by the \((k+r,l+r)\) Dubrovin–Frobenius manifold.Continuing the program of Basalaev et al. (J Phys A: Math Theor 54:115201, 2021) we associate an infinite system of commuting PDEs to these Dubrovin–Frobenius manifolds and show that these PDEs extend the dispersionless BKP hierarchy.
期刊介绍:
The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.