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Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

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Abstract.

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

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Authors and Affiliations

  1. Mathematics Department, Faculty of science, Taibah University, Al-Ula, Saudi Arabia

    Aly R. Seadawy

  2. Mathematics Department, Faculty of Science, Beni-Suef University, Beni Suef, Egypt

    Aly R. Seadawy

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  1. Aly R. Seadawy
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Correspondence to Aly R. Seadawy.

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Seadawy, A.R. Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves. Eur. Phys. J. Plus 132, 29 (2017). https://doi.org/10.1140/epjp/i2017-11313-4

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  • DOI: https://doi.org/10.1140/epjp/i2017-11313-4

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