IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i20p4351-d1263439.html
   My bibliography  Save this article

Bifurcations and Exact Solutions of the Generalized Radhakrishnan–Kundu–Lakshmanan Equation with the Polynomial Law

Author

Listed:
  • Mengke Yu

    (College of Applied Mathmatics, Chengdu University of Information Technology, Chengdu 610225, China)

  • Cailiang Chen

    (College of Applied Mathmatics, Chengdu University of Information Technology, Chengdu 610225, China)

  • Qiuyan Zhang

    (College of Applied Mathmatics, Chengdu University of Information Technology, Chengdu 610225, China
    School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu 611731, China)

Abstract

In this paper, we investigate the generalized Radhakrishnan–Kundu–Lakshmanan equation with polynomial law using the method of dynamical systems. By using traveling-wave transformation, the model can be converted into a singular integrable traveling-wave system. Then, we discuss the dynamical behavior of the associated regular system and we obtain bifurcations of the phase portraits of the traveling-wave system under different parameter conditions. Finally, under different parameter conditions, we obtain the exact periodic solutions, and the peakon, homoclinic and heteroclinic solutions.

Suggested Citation

  • Mengke Yu & Cailiang Chen & Qiuyan Zhang, 2023. "Bifurcations and Exact Solutions of the Generalized Radhakrishnan–Kundu–Lakshmanan Equation with the Polynomial Law," Mathematics, MDPI, vol. 11(20), pages 1-28, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4351-:d:1263439
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/20/4351/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/20/4351/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Melike Kaplan & Rubayyi T. Alqahtani, 2023. "Exploration of New Solitons for the Fractional Perturbed Radhakrishnan–Kundu–Lakshmanan Model," Mathematics, MDPI, vol. 11(11), pages 1-9, June.
    Full references (including those not matched with items on IDEAS)

    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.

      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:11:y:2023:i:20:p:4351-:d:1263439. 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: 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.