On classes of integrable systems and the Painlevé property. (English) Zbl 0565.35094
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.
MSC:
| 35Q58 | Other completely integrable PDE (MSC2000) |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 35G20 | Nonlinear higher-order PDEs |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
Keywords:
integrable systems; Caudrey-Dodd-Gibbon equation; Painlevé property; Bäcklund transformations; Kuperschmidt equationReferences:
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