SUBMISSION OF DECISIONS SYSTEM OF EQUATIONS OF MOTION USING TRIGONOMETRIC SERIES
https://doi.org/10.26583/vestnik.2023.251
Abstract
In this paper, in the case of two independent spatial variables, a system of equations of motion of a continuous medium with constant values of density and temperature is considered. Solutions of the Cauchy problem for this nonlinear system of partial differential equations are presented in the form of trigonometric series. An infinite system of ordinary differential equations is constructed to find the coefficients of time-dependent trigonometric series. The convergence of the trigonometric series used is proved. The theorem on multiple frequencies is also proved, describing the appearance of harmonics in the solution, which did not exist in the initial conditions.
About the Authors
S. P. Bautin
Snezhinsk Institute of Physics and Technology, National Research Nuclear University MEPhI
Russian Federation
Russian Federation
O. A. Karelina
Snezhinsk Institute of Physics and Technology, National Research Nuclear University MEPhI
Russian Federation
Russian Federation
A. G. Obukhov
Tyumen Industrial University
Russian Federation
Russian Federation
References
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Review
For citations:
Bautin S.P., Karelina O.A., Obukhov A.G. SUBMISSION OF DECISIONS SYSTEM OF EQUATIONS OF MOTION USING TRIGONOMETRIC SERIES. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2023;12(1):39-51. (In Russ.) https://doi.org/10.26583/vestnik.2023.251
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