Singularity Analysis of a Variant of the Painlev{é}--Ince Equation

Abstract

We examine by singularity analysis an equation derived by reduction using Lie point symmetries from the Euler--Bernoulli Beam equation which is the Painlevé--Ince Equation with additional terms. The equation possesses the same leading-order behaviour and resonances as the Painlevé--Ince Equation and has a Right Painlevé Series. However, it has no Left Painlev% é Series. A conjecture for the existence of Left Painlevé Series for ordinary differential equations is given.

4 pages, no figures, to appear in Applied Mathematics Letters