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

Mon, 12/01/2015 - 15:05

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.