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arXiv · 1906.00688

Singularity Analysis of a Variant of the Painlev{\'e}--Ince Equation

Amlan K Halder·Andronikos Paliathanasis·PGL Leach
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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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Amlan K Halder, Andronikos Paliathanasis, PGL Leach. 2019-06-03. Singularity Analysis of a Variant of the Painlev{\'e}--Ince Equation. https://arxiv.org/abs/1906.00688

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