IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v32y2007i2p526-537.html
   My bibliography  Save this article

The Yablonskii–Vorob’ev polynomials for the second Painlevé hierarchy

Author

Listed:
  • Demina, Maria V.
  • Kudryashov, Nikolai A.

Abstract

Special polynomials associated with rational solutions of the second Painlevé equation and other equations of its hierarchy are studied. A new method, which allows one to construct each family of polynomials is presented. The structure of the polynomials is established. Formulae for their coefficients are found. The degree of every polynomial is obtained. The main achievement of the method lies in the fact that it enables one to construct the family of polynomials corresponding to any member of the second Painlevé hierarchy. Our approach can be applied for deriving the polynomials related to rational or algebraic solutions of other nonlinear differential equations.

Suggested Citation

  • Demina, Maria V. & Kudryashov, Nikolai A., 2007. "The Yablonskii–Vorob’ev polynomials for the second Painlevé hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 526-537.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:526-537
    DOI: 10.1016/j.chaos.2006.07.032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906007338
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.07.032?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kudryashov, Nikolai A. & Efimova, Olga Yu., 2006. "Power expansions for solution of the fourth-order analog to the first Painlevé equation," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 110-124.
    2. Demina, Maria V. & Kudryashov, Nikolai A., 2007. "Power and non-power expansions of the solutions for the fourth-order analogue to the second Painlevé equation," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 124-144.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kudryashov, Nikolai A., 2009. "Special polynomials associated with rational solutions of some hierarchies," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1447-1462.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kudryashov, Nikolai A., 2009. "Special polynomials associated with rational solutions of some hierarchies," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1447-1462.

    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:eee:chsofr:v:32:y:2007:i:2:p:526-537. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.