Cherenkov-Vavilov formulation of X waves.
The field from a supersonic (or equivalently superluminal) point source in uniform motion [i.e., the Cherenkov-Vavilov (CV) effect] is shown to be equivalent to the diffractionless X-wave field. It is demonstrated that the power required to support an X wave is equivalent to the power dissipated by a CV source. In the context of the CV solution, it is clear that any supersonic or superluminal properties exhibited by X waves are purely phase effects. As a consequence, X waves cannot propagate a signal faster than the speed of waves, and thus necessarily obey the law on the finiteness of information transfer.
Walker
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Marine Physical Laboratory of the Scripps Institution of Oceanography, University of California San Diego, La Jolla, California 92093-0238, USA. scwalker@mpl.ucsd.edu
Kuperman
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