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

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 modifiled KP hierarchy written in the Fay form.

References in corpus (3)

• Double ramification cycles and integrable hierarchies
• Open intersection numbers, matrix models and MKP hierarchy
• Integrable hierarchies associated to infinite families of Frobenius manifolds