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離散数理モデリングセミナー
過去の記録 ～04/29｜次回の予定｜今後の予定 04/30～
| 担当者 | 時弘哲治, ウィロックス ラルフ |
|---|
2023年07月13日(木)
17:30-18:30 オンライン開催
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Galina Filipuk 氏 (University of Warsaw)
On the Painlevé XXV - Ermakov equation (English)
Zoomを用いてオンラインで行います．参加希望の方はウィロックスまでZoomのリンクをお尋ねください．
Galina Filipuk 氏 (University of Warsaw)
On the Painlevé XXV - Ermakov equation (English)
[ 講演概要 ]
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 to the Ermakov or the Painlevé XXV equation. The Ermakov-Painlevé XXV equation also arises from a generalized Riccati equation and the related third order linear differential equation via the Schwarzian derivative. Starting from the Riccati equation and the second-order element of the Riccati chain as the simplest examples of linearizable equations, by introducing a suitable change of variables, it is shown how the Schwarzian derivative represents a key tool in the construction of solutions. Two families of Bäcklund transformations, which link the linear and nonlinear equations under investigation, are obtained. Some analytical examples will be given and discussed.
The talk will be mainly based on the paper
S. Carillo, A. Chichurin, G. Filipuk, F. Zullo, Schwarzian derivative, Painleve XXV--Ermakov equation and Backlund transformations, accepted in Mathematische Nachrichten, https://doi.org/10.1002/mana.202200180, available at arXiv:2201.02267 [nlin.SI].
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 to the Ermakov or the Painlevé XXV equation. The Ermakov-Painlevé XXV equation also arises from a generalized Riccati equation and the related third order linear differential equation via the Schwarzian derivative. Starting from the Riccati equation and the second-order element of the Riccati chain as the simplest examples of linearizable equations, by introducing a suitable change of variables, it is shown how the Schwarzian derivative represents a key tool in the construction of solutions. Two families of Bäcklund transformations, which link the linear and nonlinear equations under investigation, are obtained. Some analytical examples will be given and discussed.
The talk will be mainly based on the paper
S. Carillo, A. Chichurin, G. Filipuk, F. Zullo, Schwarzian derivative, Painleve XXV--Ermakov equation and Backlund transformations, accepted in Mathematische Nachrichten, https://doi.org/10.1002/mana.202200180, available at arXiv:2201.02267 [nlin.SI].
