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 Painlev´e XXV– Ermakov equation via the Schwarzian derivative. The reduction to the generalized Ermakov equation is shown to arise naturally from the Painlev´e XXV–Ermakov equation. Specifically, the first order system of ordinary differential equations, equivalent to the Painlev´e XXV–Ermakov equation, is analysed by resolving points of indeterminancy of the vector field over P 1 ×P 1 .
A short note on the Painlevé XXV–Ermakov equation / Carillo, Sandra; Chichurin, Alexander; Filipuk, Galina; Zullo, Federico. - In: APPLIED MATHEMATICS LETTERS. - ISSN 0893-9659. - 131:(2022), pp. 1-8. [10.1016/j.aml.2022.108064]
A short note on the Painlevé XXV–Ermakov equation
Sandra CarilloPrimo
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2022
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 Painlev´e XXV– Ermakov equation via the Schwarzian derivative. The reduction to the generalized Ermakov equation is shown to arise naturally from the Painlev´e XXV–Ermakov equation. Specifically, the first order system of ordinary differential equations, equivalent to the Painlev´e XXV–Ermakov equation, is analysed by resolving points of indeterminancy of the vector field over P 1 ×P 1 .| File | Dimensione | Formato | |
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