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

TL;DR

This paper explores solutions to the open WDVV equations linked to type A and D Dubrovin-Frobenius manifolds, revealing their stabilization properties and connections to integrable PDE systems, including the dispersionless modified KP hierarchy.

Contribution

It establishes the stabilization condition for solutions and identifies the associated PDE systems, notably linking type A solutions to the dispersionless modified KP hierarchy.

Findings

Solutions satisfy a stabilization condition.

Type A solutions correspond to the dispersionless modified KP hierarchy.

Associated PDE systems are commuting and integrable.

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.