(Non)local Hamiltonian and symplectic structures, recursions, and hierarchies: a new approach and applications to the N=1 supersymmetric KdV equation

Details (Non)local Hamiltonian and symplectic structures, recursions, and hierarchies: a new approach and applications to the N=1 supersymmetric KdV equation (Non)local Hamiltonian and symplectic structures, recursions, and hierarchies: a new approach and applications to the N=1 supersymmetric KdV equation

2003-05-15

arxiv.org/abs/nlin/0305026v2

J. Phys. A: Math. Gen. 37 (2004), 5003-5019

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, AMS-LaTeX, Xy-pic, dvi-file to be processed by dvips. v2: nonessential improvements of exposition, title changed

Scientific paper

10.1088/0305-4470/37/18/007

Using methods of math.DG/0304245 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. The results include: a description of local and nonlocal Hamiltonian and symplectic structures, five hierarchies of symmetries, the corresponding hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. We stress that the main point of the paper is not just the results on super-KdV equation itself, but merely exposition of the efficiency of the geometrical approach and of the computational algorithms based on it.

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