Integration of acoustic wave equations for inhomogeneous media

Abstract: We obtain exact solutions of the acoustic wave equations for inhomogeneous media. Two methods for integrating these equations are proposed. The first one is based on the of the Laplace cascade method, while the second method involves reducing two-dimensional and three-dimensional models to the wave equation. In the case of plane waves, we find new solutions depending on two arbitrary functions. These solutions generalize the classical ones obtained by Euler. In the two-dimensional and three-dimensional cases, equations that can be reduced to equations with constant coefficients are found.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods