New super KdV system with the N=4 SCA as the hamiltonian structure

TL;DR

This paper introduces a new integrable super KdV system with N=4 superconformal algebra as its Hamiltonian structure, expanding the class of known SKdV systems with specific supersymmetry properties.

Contribution

It presents a novel N=2 supersymmetric extension of the N=4 SKdV hierarchy with the small N=4 SCA as the Hamiltonian structure, including Lax formulations and integrable reductions.

Findings

Constructed matrix and scalar Lax formulations.

Established relations via Miura transformation to super Boussinesq hierarchy.

Completed classification of SKdV systems with N=2 SCA as Hamiltonian structure.

Abstract

We present a new integrable extension of the a=-2, N=2 SKdV hierarchy, with the "small" N=4 superconformal algebra (SCA) as the second hamiltonian structure. As distinct from the previously known N=4 supersymmetric KdV hierarchy associated with the same N=4 SCA, the new system respects only N=2 rigid supersymmetry. We give for it both matrix and scalar Lax formulations and consider its various integrable reductions which complete the list of known SKdV systems with the N=2 SCA as the second hamiltonian structure. We construct a generalized Miura transformation which relates our system to the $\alpha = -2$, N=2 super Boussinesq hierarchy and, respectively, the ``small'' N=4 SCA to the N=2 W_3 superalgebra.