IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v232y2014icp1094-1103.html
   My bibliography  Save this article

Stability analysis of solitary wave solutions for the fourth-order nonlinear Boussinesq water wave equation

Author

Listed:
  • Helal, M.A.
  • Seadawy, A.R.
  • Zekry, M.H.

Abstract

In the present study, the nonlinear Boussinesq type equation describe the bi-directional propagation of small amplitude long capillary–gravity waves on the surface of shallow water. By using the extended auxiliary equation method, we obtained some new soliton like solutions for the two-dimensional fourth-order nonlinear Boussinesq equation with constant coefficient. These solutions include symmetrical, non-symmetrical kink solutions, solitary pattern solutions, Jacobi and Weierstrass elliptic function solutions and triangular function solutions. The stability analysis for these solutions are discussed.

Suggested Citation

  • Helal, M.A. & Seadawy, A.R. & Zekry, M.H., 2014. "Stability analysis of solitary wave solutions for the fourth-order nonlinear Boussinesq water wave equation," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1094-1103.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:1094-1103
    DOI: 10.1016/j.amc.2014.01.066
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314001039
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.01.066?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Javidi, M. & Jalilian, Y., 2008. "Exact solitary wave solution of Boussinesq equation by VIM," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1256-1260.
    2. Zhang, Huiqun, 2007. "New exact Jacobi elliptic function solutions for some nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 653-660.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Seadawy, Aly R. & Ali, Asghar & Althobaiti, Saad & Sayed, Samy, 2021. "Propagation of wave solutions of nonlinear Heisenberg ferromagnetic spin chain and Vakhnenko dynamical equations arising in nonlinear water wave models," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Seadawy, Aly R. & Bilal, M. & Younis, M. & Rizvi, S.T.R. & Althobaiti, Saad & Makhlouf, M.M., 2021. "Analytical mathematical approaches for the double-chain model of DNA by a novel computational technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Silambarasan, Rathinavel & Nisar, Kottakkaran Sooppy, 2023. "Doubly periodic solutions and non-topological solitons of 2+1− dimension Wazwaz Kaur Boussinesq equation employing Jacobi elliptic function method," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. Muhammad Shakeel & Attaullah & Mohammed Kbiri Alaoui & Ahmed M. Zidan & Nehad Ali Shah & Wajaree Weera, 2022. "Closed-Form Solutions in a Magneto-Electro-Elastic Circular Rod via Generalized Exp-Function Method," Mathematics, MDPI, vol. 10(18), pages 1-21, September.
    5. Seadawy, A.R. & El-Kalaawy, O.H. & Aldenari, R.B., 2016. "Water wave solutions of Zufiria’s higher-order Boussinesq type equations and its stability," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 57-71.
    6. Imre Ferenc Barna & Mihály András Pocsai & László Mátyás, 2022. "Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths," Mathematics, MDPI, vol. 10(13), pages 1-16, July.

    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. Jang, Bongsoo, 2009. "New exact travelling wave solutions of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 646-654.
    2. Fesanghary, M. & Pirbodaghi, T. & Asghari, M. & Sojoudi, H., 2009. "A new analytical approximation to the Duffing-harmonic oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 571-576.
    3. Zhang, Huiqun, 2009. "New exact travelling wave solutions of nonlinear evolution equation using a sub-equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 873-881.
    4. Golbabai, A. & Javidi, M., 2009. "A spectral domain decomposition approach for the generalized Burger’s–Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 385-392.
    5. Javidi, M. & Golbabai, A., 2009. "A new domain decomposition algorithm for generalized Burger’s–Huxley equation based on Chebyshev polynomials and preconditioning," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 849-857.
    6. Goh, S.M. & Noorani, M.S.M. & Hashim, I., 2009. "Efficacy of variational iteration method for chaotic Genesio system – Classical and multistage approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2152-2159.
    7. 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.
    8. 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:eee:apmaco:v:232:y:2014:i:c:p:1094-1103. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.