Infinite-Dimensional Frobenius Manifolds for 2+1 Integrable Systems

TL;DR

This paper constructs an infinite-dimensional Frobenius manifold structure on a space of pairs of functions, embedding the dispersionless 2D Toda equations into a broader integrable hierarchy, advancing the mathematical understanding of such systems.

Contribution

It introduces a novel infinite-dimensional Frobenius manifold framework for analyzing 2+1 integrable systems, expanding the geometric tools available for their study.

Findings

Established a Frobenius manifold structure on pairs of functions with specific analyticity and pole conditions.

Embedded the dispersionless 2D Toda equations into a larger integrable hierarchy.

Provided a new geometric perspective on 2+1 integrable systems.

Abstract

We introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/infinity respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobenius manifold.