IDEAS home Printed from https://ideas.repec.org/a/bla/mathna/v297y2024i1p83-101.html
   My bibliography  Save this article

Schwarzian derivative, Painlevé XXV–Ermakov equation, and Bäcklund transformations

Author

Listed:
  • Sandra Carillo
  • Alexander Chichurin
  • Galina Filipuk
  • Federico Zullo

Abstract

The role of Schwarzian derivative in the study of nonlinear ordinary differential equations is revisited. Solutions and invariances admitted by Painlevé XXV–Ermakov equation, Ermakov equation, and third‐order linear equation in a normal form are shown to be based on solutions of the Schwarzian equation. 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 are given and discussed.

Suggested Citation

  • Sandra Carillo & Alexander Chichurin & Galina Filipuk & Federico Zullo, 2024. "Schwarzian derivative, Painlevé XXV–Ermakov equation, and Bäcklund transformations," Mathematische Nachrichten, Wiley Blackwell, vol. 297(1), pages 83-101, January.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:1:p:83-101
    DOI: 10.1002/mana.202200180
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mana.202200180
    Download Restriction: no
    File URL: https://libkey.io/10.1002/mana.202200180?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:mathna:v:297:y:2024:i:1:p:83-101. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0025-584X .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.