On B type family of Dubrovin-Frobenius manifolds and their integrable systems

Abstract

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.