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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2019, Volume 60, Issue 2, Pages 220–225
DOI: https://doi.org/10.15372/PMTF20190218 (Mi pmtf472) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Waves and structures in the Boussinesq equations

O. V. Kaptsov, D. O. Kaptsov

Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036, Russia
Full-text PDF (217 kB) Citations (2)
DOI: https://doi.org/10.15372/PMTF20190218
Abstract: The classical Boussinesq equation describing gravity waves in shallow waters is under consideration. Hirota's bilinear representation is used to construct exact solutions describing wave packets, waves on solitons, and “dancing” waves. The principle of multiplying the solutions of the Hirota equation is formulated, which helps constructing more complex structures made of solitons, wave packets, and other types of waves.
Keywords: gravity waves, wave packets, solitons.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00332-а
Received: 18.07.2018
Revised: 18.07.2018
Accepted: 30.07.2018
English version:
Journal of Applied Mechanics and Technical Physics, 2019, Volume 60, Issue 2, Pages 377–381
DOI: https://doi.org/10.1134/S0021894419020184
Bibliographic databases:
Document Type: Article
UDC: 532.59+517.95
Language: Russian
Citation: O. V. Kaptsov, D. O. Kaptsov, “Waves and structures in the Boussinesq equations”, Prikl. Mekh. Tekh. Fiz., 60:2 (2019), 220–225; J. Appl. Mech. Tech. Phys., 60:2 (2019), 377–381
Citation in format AMSBIB
\Bibitem{KapKap19}
\by O.~V.~Kaptsov, D.~O.~Kaptsov
\paper Waves and structures in the Boussinesq equations
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2019
\vol 60
\issue 2
\pages 220--225
\mathnet{http://mi.mathnet.ru/pmtf472}
\crossref{https://doi.org/10.15372/PMTF20190218}
\elib{https://elibrary.ru/item.asp?id=37248723}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2019
\vol 60
\issue 2
\pages 377--381
\crossref{https://doi.org/10.1134/S0021894419020184}
Linking options:
  • https://www.mathnet.ru/eng/pmtf472
  • https://www.mathnet.ru/eng/pmtf/v60/i2/p220
    • This publication is cited in the following 2 articles:
    1. S. I. Senashov, I. L. Savostyanova, “The Exact Solutions of the Equation Describing Antiplane Plastic Flow”, Lobachevskii J Math, 42:15 (2021), 3741  crossref
    2. O. V. Kaptsov, D. O. Kaptsov, “Exact solution of Boussinesq equations for propagation of nonlinear waves”, Eur. Phys. J. Plus, 135:9 (2020)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
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