Classification of discrete equations linearizable by point transformation on a square lattice

TL;DR

This paper establishes comprehensive criteria for when nonlinear partial difference equations on a square lattice can be linearized through point transformations, and classifies all such linearizable equations up to Möbius transformations.

Contribution

It provides a complete set of linearizability conditions and a classification of all linearizable multilinear partial difference equations on four points.

Findings

Derived necessary and sufficient linearizability conditions.

Classified all linearizable multilinear equations on four points.

Identified transformations up to Möbius equivalence.

Abstract

We provide a complete set of linearizability conditions for nonlinear partial difference equations de- fined on four points and, using them, we classify all linearizable multilinear partial difference equations defined on four points up to a Mobious transformation