IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n926838.html

Traveling Wave Solutions of the Benjamin‐Bona‐Mahony Water Wave Equations

Author

Listed:
  • A. R. Seadawy
  • A. Sayed

Abstract

The modeling of unidirectional propagation of long water waves in dispersive media is presented. The Korteweg‐de Vries (KdV) and Benjamin‐Bona‐Mahony (BBM) equations are derived from water waves models. New traveling solutions of the KdV and BBM equations are obtained by implementing the extended direct algebraic and extended sech‐tanh methods. The stability of the obtained traveling solutions is analyzed and discussed.

Suggested Citation

  • A. R. Seadawy & A. Sayed, 2014. "Traveling Wave Solutions of the Benjamin‐Bona‐Mahony Water Wave Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:926838
    DOI: 10.1155/2014/926838
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/926838
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/926838?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
    ---><---

    References listed on IDEAS

    as
    1. Wazwaz, Abdul-Majid & Helal, M.A., 2005. "Nonlinear variants of the BBM equation with compact and noncompact physical structures," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 767-776.
    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. Kavitha, L. & Prabhu, A. & Gopi, D., 2009. "New exact shape changing solitary solutions of a generalized Hirota equation with nonlinear inhomogeneities," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2322-2329.
    2. Yusufoğlu, E. & Bekir, A., 2008. "The tanh and the sine–cosine methods for exact solutions of the MBBM and the Vakhnenko equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1126-1133.
    3. Memarbashi, Reza, 2008. "Numerical solution of the Laplace equation in annulus by Adomian decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 138-143.
    4. Odibat, Zaid M., 2009. "Exact solitary solutions for variants of the KdV equations with fractional time derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1264-1270.
    5. Yazhou Shi & Xiangpeng Li & Ben-gong Zhang, 2018. "Traveling Wave Solutions of Two Nonlinear Wave Equations by (G′/G)‐Expansion Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2018(1).
    6. Kumar, Vineesh & Patel, Arvind & Kumar, Monu, 2025. "Dynamics of solitons and modulation instability in a (2+1)-dimensional coupled nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 235(C), pages 95-113.
    7. Kuru, S., 2009. "Compactons and kink-like solutions of BBM-like equations by means of factorization," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 626-633.
    8. Estévez, P.G. & Kuru, Ş. & Negro, J. & Nieto, L.M., 2009. "Travelling wave solutions of the generalized Benjamin–Bona–Mahony equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2031-2040.
    9. Yusufoğlu, Elcin & Bekir, Ahmet, 2008. "Exact solutions of coupled nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 842-848.
    10. Yang, Yanhong & Wang, Yushun & Song, Yongzhong, 2018. "A new local energy-preserving algorithm for the BBM equation," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 119-130.
    11. He, Ji-Huan & Wu, Xu-Hong, 2006. "Construction of solitary solution and compacton-like solution by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 108-113.
    12. Al-Mdallal, Qasem M. & Syam, Muhammad I., 2007. "Sine–Cosine method for finding the soliton solutions of the generalized fifth-order nonlinear equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1610-1617.
    13. Yusufoğlu, E. & Bekir, A. & Alp, M., 2008. "Periodic and solitary wave solutions of Kawahara and modified Kawahara equations by using Sine–Cosine method," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1193-1197.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlaaa:v:2014:y:2014:i:1:n:926838. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.