IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i2p217-d1564340.html
   My bibliography  Save this article

Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System Approach

Author

Listed:
  • Jie Song

    (School of Mathematics and Statistics, Linyi University, Linyi 276005, China)

  • Feng Li

    (School of Mathematics and Statistics, Linyi University, Linyi 276005, China)

  • Mingji Zhang

    (Department of Mathematics, New Mexico Institution of Mining and Technology, Socorro, NM 87801, USA)

Abstract

We consider the exact traveling wave solutions for the coupled nonlinear generalized Zakharov equations. By employing the method of dynamical systems, we are able to obtain bifurcations of the phase portraits of the corresponding planar dynamical system under various parameter conditions. Based on different level curves, we derive all possible exact explicit parametric representations of bounded solutions, which include pseudo-periodic peakon, pseudo-peakon, smooth periodic wave solutions, solitary solutions, kink wave solution and the compacton solution family.

Suggested Citation

  • Jie Song & Feng Li & Mingji Zhang, 2025. "Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System Approach," Mathematics, MDPI, vol. 13(2), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:217-:d:1564340
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/2/217/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/2/217/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:13:y:2025:i:2:p:217-:d:1564340. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.