Asymptotics of the negative solutions to the general fifth painlevé equation

Abstract

The general solution of the fifth Painlevé equation

where α β γ and Δ are parameters, is an essentially new transcendental function. The behaviour of this function is far from clear, especially when all parameters are not 0. In this paper, we follow our work in [I] and obtain the asymptotics of a group of negative solutions of this equation with general real parameters.

Keywords:

• Asyrnptotics
• analysis
• solutions
• Painlevé equation

AMS:

• 34E05

Additional information

Notes on contributors

Youmin Lu

1

Bryce McLeod

2