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Construction of solitary wave solutions of some nonlinear dynamical system arising in nonlinear water wave models

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Abstract

The higher order of nonlinear partial differential equations in mathematical physics is studied. We used the analytical mathematical methods of the nonlinear (3+1)-dimensional extended Zakharov–Kuznetsov dynamical, modified KdV–Zakharov–Kuznetsov and generalized shallow water wave equations to demonstrate the efficiency and validity of the proposed powerful technique. The shallow water wave models have been applied in tidal waves and weather simulation. Exact wave solutions of these models in various forms such as Kink and anti-Kink solitons, bright–dark soliton, solitary wave and periodic solutions are constructed that have plenty of applications in diverse areas of physics. Graphically, we presented the movement of some obtained solitary wave solutions that aids in understanding the physical phenomena of these models.

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Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Taibah University, Medina, Saudi Arabia

    Aly R. Seadawy

  2. Faculty of Science, Jiangsu University, Zhenjiang, 212013, Jiangsu, People’s Republic of China

    Dianchen Lu & Naila Nasreen

Authors
  1. Aly R. Seadawy
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  2. Dianchen Lu
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  3. Naila Nasreen
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Correspondence to Aly R. Seadawy.

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This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors. The authors did not have any competing interests in this research.

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Seadawy, A.R., Lu, D. & Nasreen, N. Construction of solitary wave solutions of some nonlinear dynamical system arising in nonlinear water wave models. Indian J Phys 94, 1785–1794 (2020). https://doi.org/10.1007/s12648-019-01608-2

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  • DOI: https://doi.org/10.1007/s12648-019-01608-2

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