  Pulsars traveling at supersonic speeds are often accompanied by cometary bow
shocks seen in Halpha. We report on the first detection of a pulsar bow shock
in the far-ultraviolet (FUV). We detected it in FUV images of the nearest
millisecond pulsar J0437-4715 obtained with the Hubble Space Telescope. The
images reveal a bow-like structure positionally coincident with part of the
previously detected Halpha bow shock, with an apex at 10" ahead of the moving
pulsar. Its FUV luminosity, L(1250-2000 A) ~ 5x10^28 erg/s, exceeds the Halpha
luminosity from the same area by a factor of 10. The FUV emission could be
produced by the shocked ISM matter or, less likely, by relativistic pulsar wind
electrons confined by strong magnetic field fluctuations in the bow shock. In
addition, in the FUV images we found a puzzling extended (~3" in size)
structure overlapping with the limb of the bow shock. If related to the bow
shock, it could be produced by an inhomogeneity in the ambient medium or an
instability in the bow shock. We also report on a previously undetected X-ray
emission extending for about 5" ahead of the pulsar, possibly a pulsar wind
nebula created by shocked pulsar wind, with a luminosity L(0.5-8 keV) ~ 3x10^28
erg/s.
