L. I. Rubina, O. N. Ulyanov, “On double wave type flows”, Sibirsk. Mat. Zh., 2019, Volume 60, Number 4,Pages <nobr>859

On double wave type flows

L. I. Rubina^a, O. N. Ulyanov^ab

^a Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russia
^b Ural Federal University, Ekaterinburg, Russia

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.

UDC: 517.977

Received: 29.12.2017
Revised: 28.02.2019
Accepted: 15.05.2019

DOI: 10.33048/smzh.2019.60.412