STUDY OF A NON-STATIONARY LINEAR PLANE SUBAUDIC EQUATION

Abstract

This article presents a theoretical study of a non-stationary linear transonic equation, which is a limiting case of the Lin–Reissner–Tsien equation. The author substantiates the transition from a nonlinear velocity potential model to a linearized hyperbolic equation. Using the method of self-similar variables and separation of variables, the desired solution is reduced to the Gauss hypergeometric equation. New classes of exact analytical solutions are obtained, represented as polynomials of various degrees and elementary functions (logarithmic and power). A special case of the obtained solution for k = 2 describes the physical process of gas flow in a Laval nozzle with a curved sonic line. The results can be used for land reclamation forecasts and the calculation of gas-dynamic systems.