The Painlevé Property for Partial Differential Equations

John Weiss, M. Tabor, and George Carnevale
Center for Studies of Nonlinear Dynamics, La Jolla Institute,
La Jolla, California 92038, USA

Abstract:

In this paper we define the Painlevé property for partial differential equations and show how it determines, in a remarkably simple manner, the integrability, the Bäcklund transforms, the linearizing transforms, and the Lax pairs of three well-known partial differential equations (Burgers' equation, KdV equation, and the modified KdV equation). This indicates that the Painlevé property may provide a unified description of integrable behavior in dynamical systems (ordinary and partial differential equations), while, at the same time, providing an efficient method for determining the integrability of particular systems. PACS numbers: 02.30.Jr