IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v307y2017icp257-264.html
   My bibliography  Save this article

On the Jacobi last multipliers and Lagrangians for a family of Liénard-type equations

Author

Listed:
  • Sinelshchikov, Dmitry I.
  • Kudryashov, Nikolay A.

Abstract

We study a family of the Liénard-type equations, which can be transformed via the generalized Sundman transformations into a particular case of Painlevé–Gambier equation XXVII. We show that this equation of the Painlevé–Gambier type admits an autonomous Lagrangian, Jacobi last multiplier and first integral. As a consequence, we obtain that the corresponding family of Liénard-type equations also admits a time-independent Lagrangian, Jacobi last multiplier and first integral. We also construct the general analytical and singular solutions for members of this family of Liénard-type equations by virtue of the generalized Sundman transformations. To demonstrate applications of our results we consider several examples of the Liénard-type equations, with a generalization of the modified Emden equation among them, and construct their autonomous Lagrangians, Jacobi last multipliers and first integral as well as their general analytical solutions.

Suggested Citation

  • Sinelshchikov, Dmitry I. & Kudryashov, Nikolay A., 2017. "On the Jacobi last multipliers and Lagrangians for a family of Liénard-type equations," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 257-264.
  • Handle: RePEc:eee:apmaco:v:307:y:2017:i:c:p:257-264
    DOI: 10.1016/j.amc.2017.03.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317301819
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2017.03.010?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.

    Citations

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


    Cited by:

    1. Sinelshchikov, Dmitry I., 2020. "On linearizability via nonlocal transformations and first integrals for second-order ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Polyanin, Andrei D. & Shingareva, Inna K., 2018. "Nonlinear problems with blow-up solutions: Numerical integration based on differential and nonlocal transformations, and differential constraints," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 107-137.
    3. Ruiz, A. & Muriel, C., 2018. "On the integrability of Liénard I-type equations via λ-symmetries and solvable structures," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 888-898.

    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:apmaco:v:307:y:2017:i:c:p:257-264. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.