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Water wave solutions of Zufiria’s higher-order Boussinesq type equations and its stability

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  • Seadawy, A.R.
  • El-Kalaawy, O.H.
  • Aldenari, R.B.

Abstract

The weakly nonlinear Hamiltonian theory for two-dimensional irrotational shallow water waves is formulated. Zufiria’s higher-order Boussinesq model for waves on water of finite depth is obtained. The formulation Zufiria’s higher-order Boussinesq type equations are studied by transforming them into solvable ordinary differential equations. By implementing different types of extended direct algebraic method, we show that in fact this model has new exact solutions. An extended direct algebraic methods are applied to construct solitary wave solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:280:y:2016:i:c:p:57-71
    DOI: 10.1016/j.amc.2016.01.014
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    References listed on IDEAS

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    1. Wazwaz, Abdul-Majid, 2006. "Compactons, solitons and periodic solutions for some forms of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1005-1013.
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    4. Yomba, Emmanuel, 2006. "The modified extended Fan sub-equation method and its application to the (2+1)-dimensional Broer–Kaup–Kupershmidt equation," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 187-196.
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    Cited by:

    1. El-Sheikh, Mohamed M.A. & Seadawy, Aly R. & Ahmed, Hamdy M. & Arnous, Ahmed H. & Rabie, Wafaa B., 2020. "Dispersive and propagation of shallow water waves as a higher order nonlinear Boussinesq-like dynamical wave equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).

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