Singularity Analysis of a Variant of the Painlev{\'e}--Ince Equation
Exactly Solvable and Integrable Systems
2019-06-04 v1 Mathematical Physics
Classical Analysis and ODEs
math.MP
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.
Keywords
Cite
@article{arxiv.1906.00688,
title = {Singularity Analysis of a Variant of the Painlev{\'e}--Ince Equation},
author = {Amlan K Halder and Andronikos Paliathanasis and PGL Leach},
journal= {arXiv preprint arXiv:1906.00688},
year = {2019}
}
Comments
4 pages, no figures, to appear in Applied Mathematics Letters