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.

13 pages, LaTeX file, minor mistakes and misprints corrected

References in corpus (1)

• New Integrable Extensions of N=2 KdV and Boussinesq Hierarchies

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• A note on the third family of N=2 supersymmetric KdV hierarchies
• On gauge-equivalent formulations of N=4 SKdV hierarchy
• Hamiltonian structure and coset construction of the supersymmetric extensions of N=2 KdV hierarchy