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

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

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}-...

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Hauptverfasser:	Halder, Amlan K, Paliathanasis, Andronikos, Leach, PGL
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Classical Analysis and ODEs Mathematics - Mathematical Physics Physics - Exactly Solvable and Integrable Systems Physics - Mathematical Physics
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Zusammenfassung:	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.
DOI:	10.48550/arxiv.1906.00688