On Classes of Integrable Systems and the Painlevé Property

John Weiss
La Jolla Institute, 8950 Villa La Jolla Drive, Suite 2150,
La Jolla, CA 92037, U.S.A.
and Institute for Pure and Applied Physical Science,
University of California,San Diego, La Jolla, CA 92093, U.S.A.

Abstract:

The Caudrey-Dodd-Gibbon equation is found to possess the Painlevé property. Investigation of the Bäcklund transformations for this equation obtains the Kuperschmidt equation. A certain transformation between the Kuperschmidt and Caudrey-Dodd-Gibbon equation is obtained. This transformation is employed to define a class of p.d.e.'s that identically possesses the Painlevé property. For equations within this class Bäcklund transformations and rational solutions are investigated. In particular, the sequences of higher order KdV, Caudrey-Dobb-Gibbon, and Kuperschmidt equations are shown to possess the Painlevé property.

PACS numbers: 02.30. $+$ g