On a class of integrable deformations of the integrable hierarchy of topological type associated to a semisimple Frobenius manifold

TL;DR

This paper introduces a new class of integrable deformations for hierarchies derived from semisimple Frobenius manifolds, highlighting their polynomial tau-structures and potential universality in one-dimensional cases.

Contribution

It constructs integrable deformations with polynomial tau-structures for hierarchies associated with semisimple Frobenius manifolds, proposing a universal deformation in one dimension.

Findings

Deformations possess polynomial tau-structures.

Conjecture of universality for one-dimensional Frobenius manifolds.

New integrable hierarchies related to Frobenius manifolds.

Abstract

Given a semisimple Frobenius manifold, we construct a class of integrable deformations of its hierarchy of topological type. We show that these integrable deformations have polynomial tau-structures, and conjecture that for the one-dimensional Frobenius manifold they give a universal object for integrable deformations of the Riemann--Hopf hierarchy having a tau-structure.