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I wouldn't have said that. The motion of the wave is not the
motion of the medium! To demonstrate this, set up a rope,
clothesline style. Tie a ribbon onto it somewhere. Whack
the rope to set up a transverse wave. The wave moves along
the rope, but the ribbon moves (mostly) perpendicular to the
rope.
Next question: How does plasma wakefield acceleration (which is also
often described as "surfing") work?
http://en.wikipedia.org/wiki/Plasma_acceleration
If that isn't what you wanted to know, please ask a more specific
question.