  The fundamental solution of a variant of the three-dimensional wave equation
known as "unidirectional pulse propagation equation" (UPPE) and its paraxial
approximation is obtained. It is shown that the fundamental solution can be
presented as a projection of a fundamental solution of the wave equation to
some functional subspace. We discuss the degree of equivalence of the UPPE and
the wave equation in this respect. In particular, we show that the UPPE, in
contrast to the common belief, describes wave propagation in both longitudinal
and temporal directions, and, thereby, its fundamental solution possesses a
non-causal character.
