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

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 α = −2, N = 2 super Boussinesq hierarchy and, respectively, the “small” N = 4 SCA to the N = 2 W3 superalgebra.