Integrable systems associated to open extensions of type A and D Dubrovin–Frobenius manifolds

Abstract

Abstract We investigate the solutions to open WDVV equation, associated to type A and D Dubrovin–Frobenius manifolds. We show that these solutions satisfy some stabilization condition and associate to both of them the systems of commuting PDEs. In the type A we show that the system of PDEs constructed coincides with the dispersionless modified KP hierarchy written in the Fay form.