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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Volume 62, Issue 4, Pages 142–147
DOI: https://doi.org/10.15372/PMTF20210414 (Mi pmtf137) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Symmetries and solutions of the three-dimensional Kadomtsev–Petviashvili equation

O. V. Kaptsov, D. O. Kaptsov

Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, 660036, Krasnoyarsk, Russia
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DOI: https://doi.org/10.15372/PMTF20210414
Abstract: A group of point transformations permitted by the three-dimensional Kadomtsev–Petviashvili equation is calculated. An example of an invariant solution is given. Exact solutions for the equation under study in the form of double waves are found. The resulting solutions are expressed in terms of elementary functions and describe the interaction of a pair of solitons. Smooth bounded rational solutions are also constructed.
Keywords: Kadomtsev–Petviashvili equation, double waves, solitons.
Funding agency Grant number
Krasnoyarsk Mathematical Center 075-02-2021-1384
Received: 29.04.2021
Revised: 29.04.2021
Accepted: 31.05.2021
English version:
Journal of Applied Mechanics and Technical Physics, 2021, Volume 62, Issue 4, Pages 649–653
DOI: https://doi.org/10.1134/S0021894421040143
Bibliographic databases:
Document Type: Article
UDC: 532.59+517.95
Language: Russian
Citation: O. V. Kaptsov, D. O. Kaptsov, “Symmetries and solutions of the three-dimensional Kadomtsev–Petviashvili equation”, Prikl. Mekh. Tekh. Fiz., 62:4 (2021), 142–147; J. Appl. Mech. Tech. Phys., 62:4 (2021), 649–653
Citation in format AMSBIB
\Bibitem{KapKap21}
\by O.~V.~Kaptsov, D.~O.~Kaptsov
\paper Symmetries and solutions of the three-dimensional Kadomtsev--Petviashvili equation
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2021
\vol 62
\issue 4
\pages 142--147
\mathnet{http://mi.mathnet.ru/pmtf137}
\crossref{https://doi.org/10.15372/PMTF20210414}
\elib{https://elibrary.ru/item.asp?id=46448000}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2021
\vol 62
\issue 4
\pages 649--653
\crossref{https://doi.org/10.1134/S0021894421040143}
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    		Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
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