Integrability and the Painlevé property for low-dimensional systems

Abstract

We examine a system described by two first-order nonlinear differential equations from the point of view of integrability. The singularity analysis in the complex-time plane is used to investigate the Painlevé property, which according to the Ablowitz–Ramani–Segur conjecture is a prerequisite for integrability for infinite-dimensional systems. We show that for such low-dimensional systems, the Painlevé analysis is still a most useful guide, but integrable cases also exist which do not possess the Painlevé property.