A Lax Formalism for the Elliptic Difference Painlevé Equation

Abstract

A Lax formalism for the elliptic Painlevé 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.

v3: introduction is extended, some errors are corrected; v4: published version

References in corpus (2)

• An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations)
• Quivers and difference Painleve equations

Cited by in corpus (14)

• Geometric Aspects of Painlevé Equations
• Degenerations of Ruijsenaars-van Diejen operator and q-Painleve equations
• An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations)
• Commutation Relations and Discrete Garnier Systems
• Lax pairs of discrete Painlevé equations: $(A_2+A_1{)}^{(1)}$ case
• The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
• An Elliptic Garnier System from Interpolation
• Study of $q$-Garnier system by Padé method
• Lattice equations arising from discrete Painlevé systems. II. $A_4^{(1)}$ case
• An elliptic Garnier system
• The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I
• The noncommutative geometry of elliptic difference equations
• A Variation of the $q$-Painlevé System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$
• The Padé interpolation method applied to $q$-Painlevé equations II (differential grid version)