On B type family of Dubrovin-Frobenius manifolds and their integrable systems
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912055973380096 |
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| author | Basalaev, Alexey |
| author_facet | Basalaev, Alexey |
| contents | According to D.Zuo and an unpulished work of M.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 arXiv:2007.11974 we associate an infinite system of commuting PDEs to these Dubrovin--Frobenius manifolds and show that these PDEs extend the dispersionless BKP hierarchy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09054 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On B type family of Dubrovin-Frobenius manifolds and their integrable systems Basalaev, Alexey Exactly Solvable and Integrable Systems Mathematical Physics According to D.Zuo and an unpulished work of M.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 arXiv:2007.11974 we associate an infinite system of commuting PDEs to these Dubrovin--Frobenius manifolds and show that these PDEs extend the dispersionless BKP hierarchy. |
| title | On B type family of Dubrovin-Frobenius manifolds and their integrable systems |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2309.09054 |