Infinite-dimensional Frobenius Manifolds and Extensions of Genus-Zero Whitham Hierarchies

TL;DR

This paper constructs infinite-dimensional Frobenius manifolds from meromorphic functions on the Riemann sphere and demonstrates that their principal hierarchies extend the genus-zero Whitham hierarchies.

Contribution

It introduces a new class of infinite-dimensional Frobenius manifolds and links their hierarchies to extended genus-zero Whitham hierarchies.

Findings

Construction of infinite-dimensional Frobenius manifolds

Derivation of principal hierarchies for these manifolds

Extension of genus-zero Whitham hierarchies

Abstract

In this paper we construct a class of infinite-dimensional Frobenius manifolds in the spaces of pairs of meromorphic functions defined on certain regions of the Riemann sphere. For such Frobenius manifolds, we obtain their principal hierarchies and show them to be extensions of the genus-zero Whitham hierarchies.