New Supersymmetrizations of the Generalized KdV Hierarchies

TL;DR

This paper introduces a new supersymmetrization method for generalized KdV hierarchies, resulting in integrable, bihamiltonian supersymmetric hierarchies that extend known models and include local variants.

Contribution

It extends a supersymmetrization procedure to generalized KdV hierarchies, producing new integrable and bihamiltonian supersymmetric models with potential local forms.

Findings

Supersymmetric hierarchies are generally nonlocal, except for Boussinesque.

The hierarchies are integrable and bihamiltonian.

A local version of the supersymmetrization is also proposed.

Abstract

Recently we investigated a new supersymmetrization procedure for the KdV hierarchy inspired in some recent work on supersymmetric matrix models. We extend this procedure here for the generalized KdV hierarchies. The resulting supersymmetric hierarchies are generically nonlocal, except for the case of Boussinesque which we treat in detail. The resulting supersymmetric hierarchy is integrable and bihamiltonian and contains the Boussinesque hierarchy as a subhierarchy. In a particular realization, we extend it by defining supersymmetric odd flows. We end with some comments on a slight modification of this supersymmetrization which yields local equations for any generalized KdV hierarchy.