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 hierar chy, with the ''small'' N = 4 superconformal algebra (SCA) as the seco nd hamiltonian structure. As distinct from the previously known N = 4 supersymmetric KdV hierarchy associated with the same N = 4 SCA, the n ew system respects only N = 2 rigid supersymmetry. We give for it both matrix and scalar Lax formulations and consider its various integrabl e reductions which complete the list of known SKdV systems with the N = 2 SCA as the second hamiltonian structure. We construct a generalize d Miura transformation which relates our system to the alpha = -2, N = 2 super Boussinesq hierarchy and, respectively, the ''small'' N = 4 S CA to the N = 2 W-3 superalgebra. (C) 1997 Published by Elsevier Scien ce B.V.