I understand that a wave is most often oscillatory in character. That said, it does not have to be the case, for a wave is simply not the same as an oscillation: the former refers to a spatial pattern whereas the latter to a variation in time. We may think of a wave formed by an infinite number of motions (typically oscillatory), one at every point in space and all generally different. Now, for a non-oscillatory wave, there's just a single big disturbance that passes any one point for merely a short time. Examples of a non-oscillatory wave: a) the wave thrown off by the bow of a speedboat b) the sonic boom from a supersonic plane c) the sound wave emitted from a single gunshot. If you take a snapshot at any given time, a non-oscillatory wave pattern consists of only one localized disturbance plus tiny motions seen anywhere else. How could the wave, then, be properly propagated in time? A moment later when you do an observation yet again, you see the point where the last disturbance takes place is now virtually motionless. How could this happen at all?