Solvable Integrodifferential Equations and Their Relation to the Painlevé Conjecture

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Abstract
The Ablowitz-Ramani-Segur conjecture relates the Painlevé property, i.e., polelike local singularity structure, to integrability. As such this conjecture cannot be applied, as integrability detector, to nonlocal integrodifferential equations. We show, however, that, for the physically interesting cases of the Benjamin-Ono and intermediate long-wave equations, the Painlevé property can be recovered despite the apparent nonlocality.