IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i13p1958-d1421130.html
   My bibliography  Save this article

Exact Periodic Wave Solutions for the Perturbed Boussinesq Equation with Power Law Nonlinearity

Author

Listed:
  • Ying Kong

    (School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518107, China)

  • Jia Geng

    (School of Mathematical Sciences, Beihang University, Beijing 100191, China)

Abstract

In this paper, exact periodic wave solutions for the perturbed Boussinesq equation with power law nonlinearity are obtained for different nonlinear strengths n . When n = 1 , the periodic traveling wave solutions can be found by the definition of the Jacobian elliptic function. When n ≥ 1 , we construct a transformation to solve for the power law nonlinearity, and the periodic traveling wave solutions can be obtained by applying the extended trial equation method. In addition, we consider the limiting case where the periodicity of the periodic traveling wave solutions vanishes, and we obtain the soliton solution for n = 1 . Numerical simulations show the periodicity of the solution for the perturbed Boussinesq equation.

Suggested Citation

  • Ying Kong & Jia Geng, 2024. "Exact Periodic Wave Solutions for the Perturbed Boussinesq Equation with Power Law Nonlinearity," Mathematics, MDPI, vol. 12(13), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:1958-:d:1421130
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/13/1958/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/13/1958/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dai, Zhengde & Huang, Jian & Jiang, Murong & Wang, Shenghua, 2005. "Homoclinic orbits and periodic solitons for Boussinesq equation with even constraint," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1189-1194.
    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.
    1. Huang, Jian & Dai, Zhengde, 2008. "Homoclinic solutions for Davey-Stewartson equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 996-1002.
    2. Zeng, Xiping & Dai, Zhengde & Li, Donglong, 2009. "New periodic soliton solutions for the (3+1)-dimensional potential-YTSF equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 657-661.
    3. Dai, Zhengde & Huang, Ying & Sun, Xing & Li, Donglong & Hu, Zhenhua, 2009. "Exact singular and non-singular solitary-wave solutions for Kadomtsev–Petviashvili equation with p-power of nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 946-951.
    4. Gh. Forozani & M. Ghorveei Nosrat, 2013. "Solitary solution of modified bad and good Boussinesq equation by using of tanh and extended tanh methods," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(4), pages 497-510, August.
    5. Bratsos, A.G., 2009. "A predictor–corrector scheme for the improved Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2083-2094.

    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:13:p:1958-:d:1421130. 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.