Integrability analysis of the Emden-Fowler equation

Abstract

The Emden-Fowler equation of index n is studied utilising the techniques of Lie and Painlevé analysis. For general n information about the integrability of this equation is obtained. The link between these two types of analyses is explored. The special cases of n = -3, 2 are also examined. As a result of the Painlevé analysis new second-order equations possessing the Painlevé property are found.