A variational complex for difference equations
The authors state and prove an analogue of the Poincaré lemma for exact forms on a lattice. From the results, a variational complex for difference equations is constructed and, furthermore, it is proved to be locally exact. In order to calculate the Lagrangians for discrete Euler-Lagrange systems, homotopy maps are applied. In addition, such maps lead to a systematic technique for deriving conservation laws of a given system of difference equations, even if it is not an Euler-Lagrange system.
scientific article; zbMATH DE number 2111602