Introduction to the Painlev\'e property, test and analysis

TL;DR

This paper provides an overview of Painlevé analysis, a set of methods based on singularity properties of differential equations, for their explicit integration, with references for detailed study.

Contribution

It introduces the core concepts of Painlevé analysis and guides readers to comprehensive resources for further understanding.

Findings

Summarizes key features of Painlevé analysis

Highlights its role in explicit integration of differential equations

Provides references for detailed methodologies

Abstract

This short survey presents the essential features of what is called Painlev\'e analysis, i.e. the set of methods based on the singularities of differential equations in order to perform their explicit integration. Full details can be found in \textit{The Painlev\'e handbook} or in various lecture notes posted on arXiv.