The Fourier transform and the wave equation

TL;DR

This paper demonstrates how the Fourier transform can be used to solve the Cauchy problem for the n-dimensional wave equation, providing an elementary approach to this classical PDE problem.

Contribution

It introduces a straightforward method leveraging Fourier transform properties to solve the wave equation's initial value problem.

Findings

Solution method for n-dimensional wave equation using Fourier transform

Elementary approach simplifies classical PDE solution techniques

Provides explicit solutions for initial value problems

Abstract

We solve the Cauchy problem for the $n$-dimensional wave equation using elementary properties of the Fourier transform.