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29 March 2024
 
  » arxiv » nlin.SI/0305026

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(Non)local Hamiltonian and symplectic structures, recursions, and hierarchies: a new approach and applications to the N=1 supersymmetric KdV equation
Paul Kersten ; Iosif Krasil’shchik ; Alexander Verbovetsky ;
Date 15 May 2003
Journal J. Phys. A: Math. Gen. 37 (2004), 5003-5019 DOI: 10.1088/0305-4470/37/18/007
Subject Exactly Solvable and Integrable Systems; Differential Geometry; Mathematical Physics | nlin.SI hep-th math-ph math.DG math.MP
AbstractUsing 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.
Source arXiv, nlin.SI/0305026
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