Integrable systems of A, D and B-type Dubrovin-Frobenius manifolds

Abstract

Given a series of WDVV or open-WDVV equation solutions satisfying the certain stabilization conditions, one can construct an infinite system of commuting partial differential equations. We illustrate these fact on the examples of A and D type Dubrovin--Frobenius manifolds and their "open extensions". These give KP, a reduction of a 2-component BKP and 2D Toda hierarchies respectively. Following D.Zuo to a B_n type Coxeter group one can associate n different WDVV solutions that are not necessarily polynomial. We will prove that these Dubrovin--Frobenius structures stabilize too and present the integrable systems associated to them.