The first and second Painlevé equations of higher order and some relations between them. (English) Zbl 0962.35504
Summary: The first and second Painlevé equations of higher order are introduced. The relations between the Korteweg-de Vries hierarchies and their singular manifold equations are presented. These identities are used to search for the relations between the first and the second Painlevé equations of higher order.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
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