**DIPS 2/2003**[tex source, PostScript, PDF file, dvi]-
**Title:**The N=1 supersymmetric KdV equation: (non)local Hamiltonian and symplectic structures, recursions, and hierarchies**Authors:**Paul Kersten, Iosif Krasil'shchik, and Alexander VerbovetskyUsing methods of DIPS-6/2002 and I.S.Krasil'shchik and P.H.M.Kersten, Symmetries and recursion operators for classical and supersymmetric differential equations, Kluwer, 2000, we accomplish an extensive study of the N=1 supersymmetric Korteweg-de Vries equation. Our results generalize the ones obtained previously and include: a description of local and nonlocal Hamiltonian and symplectic structures, five hierarchies of symmetries (including a new one), the corresponding hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws.

15 pages, AMS-LaTeX, Xy-pic.

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