Integrable systems without the Painlev\'e property

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.