On Gevrey orders of formal power series solutions to the third and fifth Painlevé equations near infinity

Opuscula Mathematica

Anastasia V. Parusnikova¹ 

[1] National Research University Higher School of Economics, Bolshoi Trekhsvjatitelskii per. 3, Moscow, 109028, Russia;

关键词: Painlevé equations;    Newton polygon;    asymptotic expansions;    Gevrey orders;   

DOI  :  http://dx.doi.org/10.7494/OpMath.2014.34.3.591

来源: DOAJ

【 摘 要 】

The question under consideration is Gevrey summability of formal power series solutions to the third and fifth Painlevé equations near infinity. We consider the fifth Painlevé equation in two cases: when \(\alpha\beta\gamma\delta \neq 0\) and when \(\alpha\beta\gamma \neq 0\), \(\delta =0\) and the third Painlevé equation when all the parameters of the equation are not equal to zero. In the paper we prove Gevrey summability of the formal solutions to the fifth Painlevé equation and to the third Painlevé equation, respectively.

【 授权许可】

Unknown