All expansions of solutions to the sixth Painlevé equation near its nonsingular point
type: Item
instance of: scholarly article
title: All expansions of solutions to the sixth Painlevé equation near its nonsingular point
zbMATH Open document ID: 1181.34097
DOI: 10.1134/S1064562409030260
published in: Doklady Mathematics
publication date: 2009-10-26T00:00:00Z
review text: For the sixth Painlevé equation for all the values of its four complex parameters \(a, b, c\), and \(d\) near its nonsingular point \(x=x_0\neq 0,1,\infty\), we find all the asymptotic expansions of solutions of four types (power, powerlogarithmic, complicated, and exotic) and exponential asymptotic forms. Altogether, they form 17 families and all of them are of the power type. The other three types and exponential asymptotic forms are lacking, as must be for the Painlevé equation. Eight of these 17 families are new. The remaining nine families are known.
Mathematics Subject Classification ID: 34M55
zbMATH DE Number: 5621468
author: A. D. Bryuno
author: Irina Goryuchkina
MaRDI profile type: Publication
cites work: Asymptotic behaviour and expansions of solutions of an ordinary differential equation
cites work: Complicated expansions of solutions to an ordinary differential equation
cites work: All asymptotic expansions of solutions to the sixth Painlevé equation
cites work: Painlevé differential equations in the complex plane
full work available at URL: s1064562409030260
OpenAlex ID: W3122557285
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description: scientific article; zbMATH DE number 5621468