1993/01/12 by F. Delduc, Evgeny Ivanov, E. Ivanov · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #cond-mat #hep-th
paper · pdf · doi:10.1016/0370-2693(93)90939-f
published as Phys.Lett. B309 (1993) 312-319 · 11 pages, preprint ENSLAPP-L-415-92
arxiv created 1993/01/12 · openalex publication_date 1993/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct N=4 supersymmetric KdV equation as a hamiltonian flow on the N=4 SU(2) super Virasoro algebra. The N=4 KdV superfield, the hamiltonian and the related Poisson structure are concisely formulated in 1D N=4 harmonic superspace. The most general hamiltonian is shown to necessarily involve SU(2) breaking parameters which are combined in a traceless rank 2 SU(2) tensor. First nontrivial conserved charges of N=4 super KdV (of dimensions 2 and 4) are found to exist if and only if the SU(2) breaking tensor is a bilinear of some SU(2) vector with a fixed length proportional to the inverse of the central charge of N=4 SU(2) algebra. After the reduction to N=2 this restricted version of N=4 super KdV goes over to the a=4 integrable case of N=2 super KdV and so is expected to be integrable. We show that it is bi-hamiltonian like its N=2 prototype.