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A semi-analytic approach to study propagation and amplification of tsunami waves in mid-ocean and their run-up on shore

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Abstract

The paper proposed an effective semi-analytical approach to study tsunami wave propagation along a coast line of an ocean represented by system of nonlinear partial differential equation based on shallow water assumption. An analytical solution is obtained for system of partial differential equation describing tsunami wave propagation for different ocean depth and coastal slopes. The proposed method does not require linearization, perturbation or calculation of unneeded terms; on other hand, its transforms give system of differential equation to recursive formula and provide the series solution which converges rapidly. The obtained analytical solution closely matches with the real physical phenomena of tsunami for height and velocity of tsunami wave. To show the effectiveness and reliability of the proposed method, we have compared the obtained results with exact and analytical solution available in the literature which shows excellent agreement. The impact of ocean depth and coastal slopes on tsunami run-up and wave velocity is also discussed.

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Authors and Affiliations

  1. Department of Mathematical Sciences, P D Patel Institute of Applied Sciences, Charotar University of Science and Technology, Changa, Anand, Gujarat, 388421, India

    Yogeshwari F. Patel

  2. Sardar Vallabhai National Institute of Technology, Surat, Gujarat, 395007, India

    Jayesh M. Dhodiya

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  1. Yogeshwari F. Patel
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Patel, Y.F., Dhodiya, J.M. A semi-analytic approach to study propagation and amplification of tsunami waves in mid-ocean and their run-up on shore. Nonlinear Dyn 111, 14409–14419 (2023). https://doi.org/10.1007/s11071-023-08550-3

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  • DOI: https://doi.org/10.1007/s11071-023-08550-3

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