12 research outputs found
(Non)local Hamiltonian and symplectic structures, recursions, and hierarchies: a new approach and applications to the N=1 supersymmetric KdV equation
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.Comment: 16 pages, AMS-LaTeX, Xy-pic, dvi-file to be processed by dvips. v2:
nonessential improvements of exposition, title change
A unified approach to computation of integrable structures
We expose (without proofs) a unified computational approach to integrable
structures (including recursion, Hamiltonian, and symplectic operators) based
on geometrical theory of partial differential equations. We adopt a coordinate
based approach and aim to provide a tutorial to the computations.Comment: 19 pages, based on a talk on the SPT 2011 conference,
http://www.sptspt.it/spt2011/ ; v2, v3: minor correction
Integrable structures for a generalized Monge-Ampère equation
We consider a 3rd-order generalized Monge-Ampère equa-
tion u yyy − u 2 xxy + u xxx u xyy = 0 (which is closely related to the asso-
ciativity equation in the 2-d topological field theory) and describe all
integrable structures related to it (i.e., Hamiltonian, symplectic, and re-
cursion operators). Infinite hierarchies of symmetries and conservation
laws are constructed as well