Extension of the Adler-Bobenko-Suris classification of integrable lattice equations

TL;DR

This paper extends the Adler-Bobenko-Suris classification of integrable lattice equations by incorporating directed edges, identifying two new cases not previously classified.

Contribution

It introduces a broader classification framework for integrable lattice equations, including directed edges, and discovers two novel integrable cases.

Findings

Two new integrable lattice equations identified

Extended classification includes directed edges

Some equations are not transformable to existing forms

Abstract

The classification of lattice equations that are integrable in the sense of higher-dimensional consistency is extended by allowing directed edges. We find two cases that are not transformable via the 'admissible transformations' to the lattice equations in the existing classification.