Conservation laws of partial difference equations with two independent variables

Abstract

This paper introduces a technique for obtaining the conservation laws of a given scalar partial difference equation with two independent variables. Unlike methods that are based on Nöther's theorem, this new technique does not use symmetries. Neither does it require the difference equation to have any special structure, such as a Lagrangian, Hamiltonian or multisymplectic formulation. Instead, it uses a discrete analogue of the variational complex.