# On Boutroux's Tritronqu\'ee Solutions of the First Painlev\'e Equation

Mon, 12/01/2015 - 15:05

Speaker:

Michael Twito, University of Sydney Australia

Seminar:

Place:

2nd floor Colloquium Room, Building 216

Abstract:

The triply truncated solutions of the first Painlev\'e equation were specified by Boutroux

in his famous paper of 1913 as those having no poles (of large modulus) except in one sector

of angle $2\pi/5$. There are five such solutions and each of them can be obtained from any

other one by applying a certain symmetry transformation. One of these solutions is real on

the real axis. We will discuss a characteristic property of this solution (discovered by Prof.

Joshi, and Prof. Kitaev), different from the asymptotic description given by Boutroux.

- Last modified: 5/01/2015