First integrals, conserved vectors of nonlinear partial difference equations

Abstract

We conduct a symmetry analysis of the discrete Fitzhugh-Nagumo (FN) and the Kolmogorov Petrovskii Piskunov (KPP) equations for which the discrete versions are produced using a formal discretization method. The primary aspect of the procedure is to generate a symmetry algebra using a technique developed by Hydon. Then, we derive a method for the construction of conserved vectors or first integral vectors for the discrete equations.