On classes of integrable systems and the Painlevé property
- 1 January 1984
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 25 (1) , 13-24
- https://doi.org/10.1063/1.526009
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.Keywords
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