Wave splitting in the time domain for a radially symmetric geometry

A decomposition of the field of the wave equation in three dimensions is suggested.
This wave splitting decomposes the field into two components such
that in free space simple propagation properties are obtained. The inhomogeneous
region is assumed to have a phase velocity variation that varies only in
the radial coordinate r from the origin. The suggested wave splitting is a generalization
of the wave splitting concept in one spatial dimension. Specifically,
the propagation properties in free space in the three-dimensional wave splitting
are very analogous to the corresponding propagation properties in free
space in one dimension. The three-dimensional decomposition is illustrated
in an example of scattering by a sound-soft sphere of radius a.