If an Alcubierre drive move space does it do it permanently?

My understanding is that you aren’t moving space time from one area to another. Rather, it’s more like a wave. The Alcubierre drive would create some kind of boundary enclosing your spacecraft (a warp bubble, so to speak) that propagates through spacetime at faster-than-light speeds.

Taking this animation of a sine wave as an example:

http://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Simple_harmonic_motion_animation.gif/220px-Simple_harmonic_motion_animation.gif

The blue dot would be a point in space time. The wave is moving, but the blue dot doesn’t actually go anywhere. It just oscillates.