New super KdV system with the N=4 SCA as the 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.