Singularity Analysis of a Variant of the Painlev\'e--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 Painlev\'e--Ince Equation with additional terms. The equation possesses the same leading-order behaviour and resonances as the Painlev\'e--Ince Equation and has a Right Painlev\'e Series. However, it has no Left Painlev% \'e Series. A conjecture for the existence of Left Painlev\'e Series for ordinary differential equations is given.
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