A Lax Formalism for the Elliptic Difference Painlev\'e Equation

TL;DR

This paper introduces a Lax formalism for the elliptic Painlevé equation, leveraging geometric configurations of curves on the product of projective lines to deepen understanding of its integrability.

Contribution

It provides a novel Lax formalism for the elliptic Painlevé equation based on geometric curve configurations, advancing the theoretical framework of integrable systems.

Findings

Lax formalism explicitly constructed for elliptic Painlevé equation

Geometric interpretation via point configurations on ${\

paper_type":"theoretical"}}

Abstract

A Lax formalism for the elliptic Painlev\'e equation is presented. The construction is based on the geometry of the curves on ${\mathbb P}^1\times{\mathbb P}^1$ and described in terms of the point configurations.