Uniformization and transcendence of solutions for the first and second Painlevé hierarchies
type: Item
instance of: scholarly article
title: Uniformization and transcendence of solutions for the first and second Painlevé hierarchies
zbMATH Open document ID: 0941.34077
DOI: 10.1016/S0375-9601(97)00850-5
author: Nikolai A. Kudryashov
author: Mikhail B. Soukharev
published in: Physics Letters. A
publication date: 2000-03-08T00:00:00Z
review text: The first and second Painlevé equation hierarchies are considered. Relations between them are given. Bäcklund transformations for second Painlevé equations of higher order are presented. Some rational solutions to these equations are obtained. The indices for the first and second Painlevé equations of fourth order are found. These equations are shown to pass the Painlevé test. Lax pairs for the first and second Painlevé equations of higher order are given. The transcendence of the solutions to the first Painlevé hierarchy is discussed.
Mathematics Subject Classification ID: 34M55
Mathematics Subject Classification ID: 33E17
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 34M05
zbMATH DE Number: 1411890
zbMATH Keywords: rational solutions
zbMATH Keywords: indices
zbMATH Keywords: first and second Painlevé equations of fourth order
zbMATH Keywords: first Painlevé hierarchy
MaRDI profile type: Publication
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full work available at URL: s0375-9601(97)00850-5
OpenAlex ID: W2050380199
description: scientific article; zbMATH DE number 1411890