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arXiv · 0709.3108

Integrable systems without the Painlevé property

Alfred Ramani·Basile Grammaticos·Sébastien Tremblay
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Abstract

We examine whether the Painlevé 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-Painlevé continuous linearisable systems. We find that while these discrete systems are themselves linearisable, they possess nonconfined singularities.

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Alfred Ramani, Basile Grammaticos, Sébastien Tremblay. 2007-09-19. Integrable systems without the Painlevé property. https://doi.org/10.1088/0305-4470%2F33%2F15%2F311

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