A study on the bilinear equation of the sixth Painlev\'e transcendents

Autor:	Hosoi, Tatsuya, Sakai, Hidetaka
Rok vydání:	2023
Předmět:	Mathematics - Classical Analysis and ODEs 33E17 34M55
Druh dokumentu:	Working Paper
Popis:	The sixth Painlev\'e equation is a basic equation among the non-linear differential equations with three fixed singularities, corresponding to Gauss's hypergeometric differential equation among the linear differential equations. It is known that 2nd order Fuchsian differential equations with three singular points are reduced to the hypergeometric differential equations. Similarly, for nonlinear differential equations, we would like to determine the equation from the local behavior around the three singularities. In this paper, the sixth Painlev\'e equation is derived by imposing the condition that it is of type (H) at each three singular points for the homogeneous quadratic 4th-order differential equation. Comment: 10 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2304.13981 Zobrazit plný text záznamu View this record from Arxiv