Principal hierarchy of Infinite-dimensional Frobenius Manifold Underlying the Extended Kadomtsev-Petviashvili Hierarchy

TL;DR

This paper constructs the principal hierarchy of an infinite-dimensional Frobenius manifold related to the extended KP hierarchy, extending the genus zero Whitham hierarchy with a movable pole.

Contribution

It introduces a new principal hierarchy for an infinite-dimensional Frobenius manifold linked to the extended KP hierarchy, expanding the understanding of integrable systems.

Findings

Established the principal hierarchy for the Frobenius manifold

Connected the hierarchy to the extended KP and Whitham hierarchies

Extended the genus zero Whitham hierarchy with a movable pole

Abstract

In this paper, we construct the principal hierarchy of the infinite-dimensional Frobenius manifold underlying the extended Kadomtsev-Petviashvili hierarchy. We show that this hierarchy serves as an extension of the genus zero Whitham hierarchy with one movable pole.