Memorandum 1656

An extensive study of the N = 1 supersymmetric KDV equation

P.H.M. Kersten, I. Krasil'shchik & A. Verbovetsky

Using recently developed methods, we accomplish an extensive study of the N = 1 supersymmetric Korteweg- de Vries equation. Our results include: five hierarchies of symmetries (including a new one), the corresponding hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws and a description of local and nonlocal Hamiltonian and symplectic structures, generalizing results obtained previously.

Keywords:   Nonlinear evolution equation, variational Schouten bracket, Hamiltonian structure, recursion operator, conservation law, covering, the KdV-mKdV equation, the Boussinesq equation

Mathematics Subject Classification:   37K10, 35Q53

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