Representation of Linear Waves in Inhomogeneous Media

TL;DR

This paper investigates methods for representing linear acoustic and shallow water waves in inhomogeneous media, proposing two approaches to simplify and solve these complex equations for better understanding of wave behavior.

Contribution

It introduces two novel methods for integrating wave equations in inhomogeneous media, including a Laplace cascade approach and reduction techniques for multi-dimensional models.

Findings

Solutions for plane waves depending on two arbitrary functions

Reduced equations with constant coefficients in multi-dimensional cases

Effective methods for wave equation integration in inhomogeneous media

Abstract

The article explores the acoustic equations in inhomogeneous media and the linearized shallow water equations. Two methods for integrating these equations are proposed. The first method is based on the of the Laplace cascade method, while the second involves reducing two-dimensional and three-dimensional models to the wave equation. In the case of plane waves, solutions to some equations depending on two arbitrary functions are obtained. In the two-dimensional and three-dimensional cases, equations that can be reduced to equations with constant coefficients are found.