Time evolution of the wavelet transform of the acoustic field

In this paper we study the initial-value problem for a homogeneous acoustic wave equation in the two-dimensional space. Our approach is efficient if the initial data have multiscale structure and contain singularities and sharp edges. The wavelet transform is known to be a proper transform for analyzing such functions. We present a formula which describes the evolution with time of the wavelet transform of the spatial distribution of a solution. Our approach does not require an explicit calculation of the solution itself. A numerical example of the multiscale approach to the wave propagation is presented.