Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2019, Number 2, Pages 63–67 (Mi vmumm619)  
This article is cited in 1 scientific paper (total in 1 paper)

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Three-wave resonance in the two-dimensional stationary problem of gas dynamics

A. N. Golubyatnikov, D. V. Ukrainskii

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: In the theory of two-dimensional stationary gas dynamics, the potential isentropic motion of a perfect ideal gas on the constant homogeneous supersonic background is considered. The problem on the interaction of three traveling waves with slowly varying amplitudes and phases along the direction of the background flow is solved in the case when the sum of “harmonic” phases is exactly equal to zero. The equations of amplitude and phase variations of the waves are derived, an analytical study of their solutions is conducted. The question of what the boundary conditions should be satisfied is discussed.
Key words: three-wave resonance, amplitude-phase equations, elliptic functions, gas dynamics.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00037
Received: 02.03.2018
English version:
Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 2019, Volume 74, Issue 2, Pages 47–50
DOI: https://doi.org/10.3103/S0027133019020055
Bibliographic databases:
Document Type: Article
UDC: 534-13
Language: Russian
Citation: A. N. Golubyatnikov, D. V. Ukrainskii, “Three-wave resonance in the two-dimensional stationary problem of gas dynamics”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2019, no. 2, 63–67; Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 74:2 (2019), 47–50
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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