First integrals, conserved vectors of nonlinear partial difference equations

Abstract

We perform a symmetry analysis of some nonlinear partial difference equations (nP △ Es), where the discrete version is obtained using some discretization approach. The discrete versions of the wave, diffusion, Fisher and Huxley equations are the subject of this research. At first, the initial invariance approach is the Lie symmetry approach. The first integrals technique that Hydon introduced to be used with discrete ordinary difference equations (O △ Es) serves as our inspiration in this situation. We develop a similar technique for generating the first integral vectors of the nP △ Es without recourse to symmetry generators.