On elliptic Lax pairs and isomonodromic deformation systems for elliptic lattice equations

TL;DR

This paper extends elliptic Lax pairs for integrable lattice equations to include de-autonomisation, resulting in elliptic discrete isomonodromic deformation problems, analyzed through advanced elliptic identities.

Contribution

It introduces a de-autonomisation of elliptic Lax pairs, leading to new elliptic isomonodromic deformation systems for lattice equations.

Findings

Development of elliptic discrete isomonodromic deformation systems

Analysis of compatibility conditions using higher order elliptic identities

Extension of previous elliptic Lax pair frameworks

Abstract

In a previous article [N. Delice, F.W. Nijhoff and S. Yoo-Kong, J. Phys. A: Math. Theor. 48(3) (2015), 035206] a novel class of elliptic Lax pairs for integrable lattice equations was introduced. The present article proposes a de-autonomisation of those Lax pairs leading to a class of elliptic discrete isomonodromic deformation problems. We analyse the systems of compatibility conditions using some (possibly novel) higher order elliptic identities.