Linearizability of Nonlinear Equations on a Quad-Graph by a Point, Two Points and Generalized Hopf-Cole Transformations

TL;DR

This paper introduces linearizability tests for nonlinear partial difference equations on quad-graphs using point, two-point, and generalized Hopf-Cole transformations, and applies these tests to various complex examples.

Contribution

It develops new linearizability tests for nonlinear equations on quad-graphs and demonstrates their effectiveness on nontrivial cases.

Findings

Successfully identifies linearizable equations using the proposed tests

Extends the applicability of linearization methods to complex examples

Provides a framework for analyzing nonlinear equations on quad-graphs

Abstract

In this paper we propose some linearizability tests of partial difference equations on a quad-graph given by one point, two points and generalized Hopf-Cole transformations. We apply the so obtained tests to a set of nontrivial examples.