Super tau-covers of bihamiltonian integrable hierarchies

TL;DR

This paper introduces super tau-covers for bihamiltonian integrable hierarchies, extending their Hamiltonian structures and symmetries, including for the KdV hierarchy and hierarchies from Frobenius manifolds.

Contribution

It constructs super tau-covers for arbitrary Frobenius manifold hierarchies and the KdV hierarchy, extending their symmetry structures to include Virasoro symmetries.

Findings

Super tau-covers include local and non-local Hamiltonian structures.

Virasoro symmetries extend to super tau-covers.

Construction applies to hierarchies from Frobenius manifolds and KdV.

Abstract

We consider a certain super extension, called the super tau-cover, of a bihamiltonian integrable hierarchy which contains the Hamiltonian structures including both the local and non-local ones as odd flows. In particular, we construct the super tau-cover of the principal hierarchy associated with an arbitrary Frobenius manifold, and the super tau-cover of the Korteweg-de Vries (KdV) hierarchy. We also show that the Virasoro symmetries of these bihamiltonan integrable hierarchies can be extended to symmetries of the associated super tau-covers.