On special solutions to the Ermakov-Painlevé XXV equation
Artykuł naukowy w czasopiśmie recenzowanyCzasopismo: Random Matrices-Theory and Applications (ISSN: 2010-3263)
Współautorzy: Galina Filipuk
Rok wydania: 2024
Tom: 13
Numer czasopisma: 1
Strony od-do: 2450001
Streszczenie: In this paper we study a nonlinear second order ordinary differential equation which we call the Ermakov-Painlevé XXV equation since under certain restrictions on its coefficients it can be reduced either to the Ermakov or the Painlevé XXV equation. The Ermakov-Painlevé XXV equation arises from a generalized Riccati equation and the related third order linear differential equation via the Schwarzian derivative. The generalized Riccati equation has two families of Riccati solutions and we study the corresponding solutions to the Ermakov-Painlevé XXV equation. We show that one of these families appears only in the Ermakov case. We give examples of the Ermakov-Painlevé XXV equations and show how to construct their solutions expressed in terms of elementary or in terms of the classical special functions.
Słowa kluczowe: Riccati equation, generalized Riccati equation, Painlevé XXV equation, Ermakov equation, special functions, linear differential equations
DOI: https://doi.org/10.1142/S2010326324500011
Cytowanie w formacie Bibtex:
@article{1,
author = "Aliaksandr Chychuryn and Galina Filipuk",
title = "On special solutions to the Ermakov-Painlevé XXV equation",
journal = "Random Matrices-Theory and Applications",
year = "2024",
number = "1",
pages = "2450001"
}
Cytowanie w formacie APA:
Chychuryn, A. and Galina Filipuk(2024). On special solutions to the Ermakov-Painlevé XXV equation. Random Matrices-Theory and Applications, 1, 2450001.