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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 4, Pages 859–873
DOI: https://doi.org/10.33048/smzh.2019.60.412 (Mi smj3120) 		 
On double wave type flows

L. I. Rubinaa, O. N. Ulyanovab

a Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russia
b Ural Federal University, Ekaterinburg, Russia
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DOI: https://doi.org/10.33048/smzh.2019.60.412
Abstract: We study the potential double wave equation and the system of spatial double wave equations. In the class of solutions of multiple wave type, these equations are reduced to an ODE and the system of ODEs respectively. We find some exact solutions and obtain formulas for the contact lines of the corresponding double waves with a simple wave, show that in a neighborhood of an arbitrary point in the plane of self-similar variables there exists a special flow of potential double wave type, and construct a spatial double wave type flow around a specified smooth body.
Keywords: nonlinear PDEs, potential double waves, spatial double waves, method of characteristics, exact solutions.
Received: 29.12.2017
Revised: 28.02.2019
Accepted: 15.05.2019
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 4, Pages 673–684
DOI: https://doi.org/10.1134/S0037446619040128
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: L. I. Rubina, O. N. Ulyanov, “On double wave type flows”, Sibirsk. Mat. Zh., 60:4 (2019), 859–873; Siberian Math. J., 60:4 (2019), 673–684
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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