Rigorous analytical approximation of tritronquee solution to Painleve-1 and the first singularity

Abstract

We use a recently developed method to determine approximate expression for tritronquée solution for P-1: $y^{\prime \prime }+6y^2-x=0$ in a domain $D$ with rigorous bounds. In particular we rigorously confirm the location of the closest singularity from the origin to be at $x=-\frac{770766}{323285}=-2.3841687675\cdots$ to within $5\times 10^{-6}$ accuracy, in agreement with previous numerical calculation.

Cited by in corpus (1)

• Location of Poles for the Hastings-McLeod Solution to the Second Painlevé Equation