Integrable systems without the Painlevé property

Details Integrable systems without the Painlevé property Integrable systems without the Painlevé property

2007-09-19

arxiv.org/abs/0709.3108v1

J. Phys. A: Math. Gen., 33, No 15 (2000), 3045-3052

Physics

Mathematical Physics

Scientific paper

10.1088/0305-4470/33/15/311

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.

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