Padé approximations for Painlevé I and II transcendents
type: Item
instance of: scholarly article
title: Padé approximations for Painlevé I and II transcendents
zbMATH Open document ID: 1185.34139
published in: Theoretical and Mathematical Physics
publication date: 2009-11-06T00:00:00Z
review text: The author shows, that the Painlevé I and II equations can be transformed into a form to which the Fair-Luke algorithm is applicable to find the Padé approximate solutions. It appears that the numerical implementation of this algorithm works fast even on the PC of initial level. By this way, the author received the distribution of poles for the well-known Ablowitz- Segur and Hastings-McLeod solutions of the Painlevé II equation and suggested some conjectures. The algorithm allows checking other analytic properties of the Painlevé transcendents, such as the asymptotic behaviour at infinity in the complex plane.
reviewed by: Mykola Grygorenko
Mathematics Subject Classification ID: 34M55
zbMATH DE Number: 5626849
zbMATH Keywords: Painlevé equation
zbMATH Keywords: meromorphic solution
zbMATH Keywords: distribution of poles
zbMATH Keywords: Padé approximation
zbMATH Keywords: continued fraction
zbMATH Keywords: Riemann-Hilbert problem
author: V. Yu. Novokshenov
MaRDI profile type: Publication
full work available at URL: s11232-009-0073-8
OpenAlex ID: W2071415804
cites work: Q5394330
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cites work: On Boutroux's Tritronquée Solutions of the First Painlevé Equation
cites work: On orthogonal and symplectic matrix ensembles
DOI: 10.1007/S11232-009-0073-8
description: scientific article; zbMATH DE number 5626849