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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2023, Volume 64, Issue 2, Pages 48–63
DOI: https://doi.org/10.15372/PMTF202215130
(Mi pmtf1255)
 

This article is cited in 1 scientific paper (total in 1 paper)

Phase and amplitude characteristics of nonlinear dispersion models improved precision

Z. I. Fedotova, G. S. Khakimzianov

Federal Research Center for Information and Computing Technologies, Novosibirsk, Russia
References:
Abstract: The properties of the dispersion relations for two new fully nonlinear weakly dispersive shallow water models are studied, for which, with certain parameters, it is possible to obtain the fourth, sixth, or eighth order of accuracy of the approximation of the phase velocity of the three-dimensional potential current model. For the hierarchy of shallow water models, under the assumption of a slightly changing shape of the bottom, formulas are obtained that establish the relationship between the rate of change in the wave amplitude and the rate of change in the thickness of the liquid layer, and the dependences of the amplitude and length of the incident wave on the depth of the water area are also derived. It is shown that the new model of the fourth order long-wavelength approximation with the eighth order of accuracy of the dispersion relation provides the best approximation of the considered characteristics in the case of both a horizontal bottom and a variable-shaped bottom.
Keywords: long surface waves, nonlinear dispersion equations, dispersion relation, phase velocity, Green's law.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation
The work was carried out within the framework of the state task of the Ministry of Science and Higher Education of the Russian Federation for the Federal Research Center for Information and Computing Technologies.
Received: 25.04.2022
Revised: 08.09.2022
Accepted: 26.09.2022
English version:
Journal of Applied Mechanics and Technical Physics, 2023, Volume 64, Issue 2, Pages 216–229
DOI: https://doi.org/10.1134/S0021894423020062
Bibliographic databases:
Document Type: Article
UDC: 532.59
Language: Russian
Citation: Z. I. Fedotova, G. S. Khakimzianov, “Phase and amplitude characteristics of nonlinear dispersion models improved precision”, Prikl. Mekh. Tekh. Fiz., 64:2 (2023), 48–63; J. Appl. Mech. Tech. Phys., 64:2 (2023), 216–229
Citation in format AMSBIB
\Bibitem{FedKha23}
\by Z.~I.~Fedotova, G.~S.~Khakimzianov
\paper Phase and amplitude characteristics of nonlinear dispersion models improved precision
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2023
\vol 64
\issue 2
\pages 48--63
\mathnet{http://mi.mathnet.ru/pmtf1255}
\crossref{https://doi.org/10.15372/PMTF202215130}
\elib{https://elibrary.ru/item.asp?id=50441314}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2023
\vol 64
\issue 2
\pages 216--229
\crossref{https://doi.org/10.1134/S0021894423020062}
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  • https://www.mathnet.ru/eng/pmtf/v64/i2/p48
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
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    Abstract page:44
    References:16
    First page:3
     
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