2019/02/21 by Nalini Joshi, Joshi, Nalini, Nobutaka Nakazono +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1902.07842
openalex publication_date 2019/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Discrete Painlevé equations are nonlinear, nonautonomous difference equations of second-order. They have coefficients that are explicit functions of the independent variable n and there are three different types of equations according to whether the coefficient functions are linear, exponential or elliptic functions of n. In this paper, we focus on the elliptic type and give a review of the construction of such equations on the E8 lattice. The first such construction was given by Sakai \citeSakaiH2001:MR1882403. We focus on recent developments giving rise to more examples of elliptic discrete Painlevé equations.