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Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths

Author

Listed:
  • Imre Ferenc Barna

    (Wigner Research Centre for Physics, Konkoly–Thege Miklós út 29-33, H-1121 Budapest, Hungary)

  • Mihály András Pocsai

    (Wigner Research Centre for Physics, Konkoly–Thege Miklós út 29-33, H-1121 Budapest, Hungary
    Institute of Physics, Department of Physics, University of Pécs, Ifjúság útja 6, H-7624 Pécs, Hungary)

  • László Mátyás

    (Department of Bioengineering, Faculty of Economics, Socio-Human Sciences and Engineering, Sapientia Hungarian University of Transylvania, Libertătii Sq. 1, 530104 Miercurea Ciuc, Romania)

Abstract

We investigate a hydrodynamic equation system which—with some approximation—is capable of describing the tsunami propagation in the open ocean with the time-dependent self-similar Ansatz. We found analytic solutions of how the wave height and velocity behave in time and space for constant and linear seabed functions. First, we study waves on open water, where the seabed can be considered relatively constant, sufficiently far from the shore. We found original shape functions for the ocean waves. In the second part of the study, we also consider a seabed which is oblique. Most of the solutions can be expressed with special functions. Finally, we apply the most common traveling wave Ansatz and present relative simple, although instructive solutions as well.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2311-:d:854007
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    References listed on IDEAS

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    1. 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.
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