Linear degree growth in lattice equations

TL;DR

This paper investigates the degree growth of lattice equations, proposing recurrence relations to identify which are linearizable by demonstrating their linear growth patterns.

Contribution

It introduces conjectured recurrence relations for degree growth, aiding in the classification of linearizable lattice equations.

Findings

Recurrence relations for degree growth are proposed.

Linear growth indicates linearizability of lattice equations.

Method helps identify linearizable equations based on degree growth.

Abstract

We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth and hence are linearizable.