In this preprint we find this:
Wave propagation in odd-dimensional space is fundamentally different from wave propagation in evendimensionaleven-dimensional space. When the space dimension $\mathrm D$ is odd and $\mathrm{D} > 1,$ waves obey Huygens’ principle [1, 2]; that is, waves created by an instantaneous point source at $t = 0$ (e.g., a light pulse) take the form of an expanding bubble. After the wavefront passes by, the medium instantly returns to quiescence. An observer sees blackness until the wave arrives, sees an instantaneous flash as the wave passes by, and immediately afterward sees blackness again [see Fig. 1(a)]. Such a wave propagates on the surface of the light cone. In contrast, in even-dimensional space an instantaneous point source gives rise to a wave that develops a tail. An observer sees blackness until the wave arrives and then sees a flash. However, the medium does not immediately return to quiescence; rather, the wave amplitude decays to $0$ like $t^{-\alpha},$ where $\alpha > 0$ depends on $\mathrm D.$