Elliptic asymptotics in q-discrete Painlevé equations

2019/01/24 by Nalini Joshi, Joshi, Nalini, Elynor Liu +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Differential Equations and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1901.08279

openalex publication_date 2019/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behaviour of two multiplicative- (q-) discrete Painlevé equations as their respective independent variable goes to infinity. It is shown that the generic asymptotic behaviours are given by elliptic functions. We extend the method of averaging to these equations to show that the energies are slowly varying. The Picard-Fuchs equation is derived for a special case of q-P_{\rm III}

Citations

• A differential equation for orthogonal polynomials
• Quicksilver Solutions of aq‐Difference First Painlevé Equation

Related

• Elliptic asymptotic behaviour of q-Painlevé transcendents
• A Local Asymptotic Analysis of the First Discrete Painlevé Equation as the Discrete Independent Variable Approaches Infinity
• Asymptotic approach for the rigid condition of appearance of the oscillations in the solution of the Painleve-2 equation
• An Overview of Geometric Asymptotic Analysis of Continuous and Discrete Painlevé Equations
• Asymptotic Series for Some PainlevÉ VI Solutions