General solutions to the equations of acoustics in inhomogeneous media and gas dynamics

TL;DR

This paper develops a method using Riemann approach and Euler transformations to find new exact solutions for one-dimensional acoustics and gas dynamics equations in inhomogeneous media, with solutions depending on arbitrary functions.

Contribution

It introduces a novel approach to derive exact solutions for inhomogeneous acoustics and gas dynamics equations using hyperbolic equations and transformations.

Findings

New exact solutions depending on two arbitrary functions

Reduction of gas dynamics equations to a second-order hyperbolic form

Application of Euler transformations to construct solutions

Abstract

This paper considers one-dimensional equations of acoustics equations of inhomogeneous media and the system of gas dynamics equations with constant entropy. Using the Riemann approach, the gas dynamics equations are reduced to a second-order linear hyperbolic equation with variable coefficients. Solutions to this equation are constructed using Euler transformations. This allows us to find new exact solutions of the equations of acoustics and gas dynamics, depending on two arbitrary functions.