1996/07/25 by Nalini Joshi, Joshi, Nalini
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.solv-int/9607006
openalex publication_date 1996/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The first discrete Painlevé equation (dPI), which appears in a model of quantum gravity, is an integrable nonlinear nonautonomous difference equation which yields the well known first Painlevé equation (PI) in a continuum limit. The asymptotic study of its solutions as the discrete time-step n→∞ is important both for physical application and for checking the accuracy of its role as a numerical discretization of PI. Here we show that the asymptotic analysis carried out by Boutroux (1913) for PI as its independent variable approaches infinity can also be achieved for dPI as its discrete independent variable approaches the same limit.