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

According to Zuo and an unpublished work of Bertola, there is a two-index series of Dubrovin–Frobenius manifold structures associated to a B-type Coxeter group.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 \((k+r,l+r)\) $(k+r,l+r)$ 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.