IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i16p2474-d1453792.html
   My bibliography  Save this article

The Period Function of the Generalized Sine-Gordon Equation and the Sinh-Poisson Equation

Author

Listed:
  • Lin Lu

    (School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, China)

  • Xiaokai He

    (School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, China)

  • Xing Zhou

    (School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, China)

Abstract

In this paper, we consider the generalized sine-Gordon equation ψ t x = ( 1 + a ∂ x 2 ) sin ψ and the sinh-Poisson equation u x x + u y y + σ sinh u = 0 , where a is a real parameter, and σ is a positive parameter. Under different conditions, e.g., a = 0 , a ≠ 0 , and σ > 0 , the periods of the periodic wave solutions for the above two equations are discussed. By the transformation of variables, the generalized sine-Gordon equation and sinh-Poisson equations are reduced to planar dynamical systems whose first integral includes trigonometric terms and exponential terms, respectively. We successfully handle the trigonometric terms and exponential terms in the study of the monotonicity of the period function of periodic solutions.

Suggested Citation

  • Lin Lu & Xiaokai He & Xing Zhou, 2024. "The Period Function of the Generalized Sine-Gordon Equation and the Sinh-Poisson Equation," Mathematics, MDPI, vol. 12(16), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2474-:d:1453792
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/16/2474/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/16/2474/
    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:12:y:2024:i:16:p:2474-:d:1453792. 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.