Linearization through symmetries for discrete equations

TL;DR

This paper introduces a symmetry-based method to determine if discrete equations can be linearized through point or Cole-Hopf transformations, providing explicit transformations when possible, with applications to four-point lattice equations.

Contribution

It presents a novel symmetry approach to check and construct linearizing transformations for discrete equations, including explicit examples.

Findings

Symmetry approach effectively identifies linearizable discrete equations.

Explicit linearizing transformations are derived for specific equations.

Method applied successfully to equations on four lattice points.

Abstract

We show that one can define through the symmetry approach a procedure to check the linearizability of a difference equation via a point or a discrete Cole-Hopf transformation. If the equation is linearizable the symmetry provides the linearizing transformation. At the end we present few examples of applications for equations defined on four lattice points.