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Dispersive and propagation of shallow water waves as a higher order nonlinear Boussinesq-like dynamical wave equations

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  • El-Sheikh, Mohamed M.A.
  • Seadawy, Aly R.
  • Ahmed, Hamdy M.
  • Arnous, Ahmed H.
  • Rabie, Wafaa B.

Abstract

The propagation of small amplitude long capillary–gravity waves on the surface of shallow water described by the higher order nonlinear Boussinesq type wave equation. This model is arising in mathematical physics, shallow water waves, fluid dynamics and fluid flow. We applied the modified Jacobi elliptic function expansion method to obtained exact solutions in the type of solitary wave and elliptic functions solutions. These solutions helps the mathematicians and physicians to understand the physical phenomena of this model. This technique can be utilized on other models to launch further exclusively novel solutions for other categories of nonlinear PDEs occurring in mathematical Physics.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315195
    DOI: 10.1016/j.physa.2019.122662
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    References listed on IDEAS

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    1. Seadawy, Aly R., 2016. "Stability analysis solutions for nonlinear three-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov equation in a magnetized electron–positron plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 44-51.
    2. Seadawy, Aly R., 2015. "Nonlinear wave solutions of the three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 124-131.
    3. 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.
    4. Ali Akgül & Adem Kılıçman & Mustafa Inc, 2013. "Improved ( )-Expansion Method for the Space and Time Fractional Foam Drainage and KdV Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, September.
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    Cited by:

    1. Wafaa B. Rabie & Hamdy M. Ahmed & Walid Hamdy, 2023. "Exploration of New Optical Solitons in Magneto-Optical Waveguide with Coupled System of Nonlinear Biswas–Milovic Equation via Kudryashov’s Law Using Extended F-Expansion Method," Mathematics, MDPI, vol. 11(2), pages 1-28, January.
    2. 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).

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