On non-multiaffine consistent-around-the-cube lattice equations

TL;DR

This paper demonstrates that certain integrable involutive maps can generate consistent-around-the-cube lattice equations that are not multiaffine, expanding the class of known integrable lattice models.

Contribution

It introduces non-multiaffine lattice equations derived from integrable involutive maps, challenging the assumption that such equations must be multiaffine.

Findings

Identified non-multiaffine consistent-around-the-cube lattice equations

Connected these equations to the lattice potential KdV via nonlocal transformations

Expanded the understanding of integrable lattice models

Abstract

We show that integrable involutive maps, due to the fact they admit three integrals in separated form, can give rise to equations, which are consistent around the cube and which are not in the multiaffine form assumed in papers [1, 2]. Lattice models, which are discussed here, are related to the lattice potential KdV equation by nonlocal transformations (discrete quadratures).