A local asymptotic analysis of the discrete first Painlevé equation as the discrete independent variable approaches infinity
type: Item
instance of: scholarly article
title: A local asymptotic analysis of the discrete first Painlevé equation as the discrete independent variable approaches infinity
zbMATH Open document ID: 0906.39002
author: Nalini Joshi
published in: Methods and Applications of Analysis
publication date: 1998-04-27T00:00:00Z
review text: The discrete first Painlevé equation which appears in a model of quantum gravity is an integrable nonlinear nonautonomous difference equation which yields the well known first Painlevé equation in a continuum limit. The asymptotic study of its solutions as the discrete time-step \(n\to \infty\) is important both for physical applications and for checking the accuracy of its role as a numerical discretization of the Painlevé equation. In this paper it is shown that the asymptotic analysis carried out by \textit{P. Boutroux} [Ann. de l'Éc. Norm. (3) 30, 255-375 (1913; JFM 44.0382.02)] for the Painlevé equation as its independent variable approaches infinity also can be achieved for discrete Painlevé equation as its discrete independent variable approaches the same circuit.
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 81V17
Mathematics Subject Classification ID: 83C45
zbMATH DE Number: 1129310
zbMATH Keywords: discrete first Painlevé equation
zbMATH Keywords: quantum gravity
zbMATH Keywords: integrable nonlinear nonautonomous difference equation
zbMATH Keywords: asymptotic
zbMATH Keywords: JFM 44.0382.02
reviewed by: Stefan Balint
MaRDI profile type: Publication
DOI: 10.4310/MAA.1997.V4.N2.A2
description: scientific article; zbMATH DE number 1129310