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

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  • 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
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    References listed on IDEAS

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    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.
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    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. 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.
    3. 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).
    4. 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.
    5. 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).
    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.

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