New Integrable Extensions of N=2 KdV and Boussinesq Hierarchies

TL;DR

This paper introduces new integrable supersymmetric systems by extending existing N=2 hierarchies, including a novel N=4 super KdV Lax operator, advancing the understanding of supersymmetric integrability.

Contribution

It constructs new N=2 supersymmetric integrable systems through junction of pseudo-differential Lax operators, including an N=4 super KdV Lax operator and extensions of Boussinesq hierarchies.

Findings

Derived Lax operator for N=4 super KdV

Extended N=2 Boussinesq hierarchies

Proposed minimal N=4 supersymmetric extension

Abstract

We construct a new variety of $N=2$ supersymmetric integrable systems by junction of pseudo-differential superspace Lax operators for $a=4$, $N=2$ KdV and multi-component $N=2$ NLS hierarchies. As an important particular case, we obtain Lax operator for $N=4$ super KdV system. A similar extension of one of $N=2$ super Boussinesq hierarchies is given. We also present a minimal $N=4$ supersymmetric extension of the second flow of $N=4$ KdV hierarchy and comment on its possible integrability.