Infinite-dimensional Frobenius manifolds underlying an extension of the dispersionless Kadomtsev–Petviashvili hierarchy

Abstract

We construct a class of infinite-dimensional Frobenius manifolds on the spaces of pairs of meromorphic functions with a pole at infinity and a movable pole. Such Frobenius manifolds are shown to be underlying the Whitham hierarchy, which is an extension of the dispersionless Kadomtsev–Petviashvili hierarchy.