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Graded differential equations and their deformations: A computational theory for recursion operators
Authors:I. S. Krasil'shchik  P. H. M. Kersten
Affiliation:(1) Moscow Institute for Municipal Economy and Civil Engineering, Moscow, Russia;(2) Department of Applied Mathematics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Abstract:An algebraic model for nonlinear partial differential equations (PDE) in the category ofn-graded modules is constructed. Based on the notion of the graded Frölicher-Nijenhuis bracket, cohomological invariants Hxdtri*(A) are related to each object (A, xdtri) of the theory. Within this framework, Hxdtri0 (A) generalizes the Lie algebra of symmetries for PDE's, while Hxdtri1(A) are identified with equivalence classes of infinitesimal deformations. It is shown that elements of a certain part of Hxdtri1(A) can be interpreted as recursion operators for the object (A, xdtri), i.e. operators giving rise to infinite series of symmetries. Explicit formulas for computing recursion operators are deduced. The general theory is illustrated by a particular example of a graded differential equation, i.e. the Super KdV equation.Tverskoy-Yamskoy per. 14, Apt. 45, 125047 Moscow, Russia.
Keywords:58F07  58G07  58H10  58H15  58G37  58A50  35Q53  35Q55  35Q58  58G35  16W55
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