This article is cited in 2 papers

Integration of equations of acoustics of inhomogeneous media

O. V. Kaptsov

Federal Research Center for Information and Computational Technologies, Novosibirsk, Russia

Abstract: We propose two approaches to integrating linear acoustic equations in inhomogeneous media. The first is based on the Laplace cascade method. For one-dimensional nonstationary equations, new solutions are obtained that depend on two arbitrary functions. These solutions are generalizations of relatively undistorted waves. In the two-dimensional case, conformal maps are used that allow reducing some equations with variable coefficients to equations with constant coefficients. Special three-dimensional equations can also be transformed to a wave equation.

Keywords: acoustic equations, Laplace cascade method, conformal maps, exact solutions.

MSC: 35Q35, 76M60

Received: 12.01.2025
Revised: 14.02.2025

DOI: 10.4213/tmf10887

 English version: Theoretical and Mathematical Physics, 2025, 223:2, 770–781

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