Symbolic Computation of Conserved Densities, Generalized Symmetries, and Recursion Operators for Nonlinear Differential-Difference Equations
Willy Hereman, Jan A. Sanders, Jack Sayers, Jing Ping Wang
Abstract
Algorithms for the symbolic computation of conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations are presented. In the algorithms we use discrete versions of the Frechet and variational derivatives, as well as discrete Euler and homotopy operators. The algorithms are illustrated for prototypical nonlinear lattices, including the Kac-van Moerbeke (Volterra) and Toda lattices. Results are shown for the modified Volterra and Ablowitz-Ladik lattices.
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