Solutions of the second member of the Riccati chain and of the corresponding third order linear differential equation are related to solutions of the so-called Painlevé XXV–Ermakov equation via the Schwarzian derivative. The reduction to the generalised Ermakov equation is shown to arise naturally from the Painlevé XXV–Ermakov equation. Specifically, the first order system of ordinary differential equations, equivalent to the Painlevé XXV–Ermakov equation, is analysed by resolving points of indeterminacy of the vector field over P1xP1.
A short note on the Painlevé XXV–Ermakov equation
Zullo, Federico
2022-01-01
Abstract
Solutions of the second member of the Riccati chain and of the corresponding third order linear differential equation are related to solutions of the so-called Painlevé XXV–Ermakov equation via the Schwarzian derivative. The reduction to the generalised Ermakov equation is shown to arise naturally from the Painlevé XXV–Ermakov equation. Specifically, the first order system of ordinary differential equations, equivalent to the Painlevé XXV–Ermakov equation, is analysed by resolving points of indeterminacy of the vector field over P1xP1.File in questo prodotto:
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Descrizione: Applied Mathematics Letters, 131, (2022), 108064
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