Integrable systems without the Painlev\'e property
Mathematical Physics
2013-07-10 v1 math.MP
Abstract
We examine whether the Painlev\'e property is a necessary condition for the integrability of nonlinear ordinary differential equations. We show that for a large class of linearisable systems this is not the case. In the discrete domain, we investigate whether the singularity confinement property is satisfied for the discrete analogues of the non-Painlev\'e continuous linearisable systems. We find that while these discrete systems are themselves linearisable, they possess nonconfined singularities.
Keywords
Cite
@article{arxiv.0709.3108,
title = {Integrable systems without the Painlev\'e property},
author = {Alfred Ramani and Basile Grammaticos and Sébastien Tremblay},
journal= {arXiv preprint arXiv:0709.3108},
year = {2013}
}