Application of uniform asymptotics to the connection formulas of the fifth Painlev\'{e} equation

TL;DR

This paper uses uniform asymptotics to rigorously derive connection formulas for a special solution of the fifth Painlevé equation, simplifying previous proofs based on isomonodromy and WKB methods.

Contribution

It provides a simpler, more rigorous proof of connection formulas for a special Painlevé V solution using uniform asymptotics.

Findings

Connection formulas are rigorously established.

Method simplifies previous proofs.

Enhances understanding of Painlevé V solutions.

Abstract

We apply the uniform asymptotics method proposed by Bassom, Clarkson, Law and McLeod to a special Painlev\'{e} V equation, and we provide a simpler and more rigorous proof of the connection formulas for a special solution of the equation, which have been established earlier by McCoy and Tang via the isomonodromy and WKB methods.