  We explore analytically the structure of relativistic shock and solitary wave
solutions in collisionless plasmas. In the wave frame of reference, a cold
plasma is flowing from one end and impacting on a low velocity plasma. First we
show that under astrophysical conditions, a cold electron-positron plasma is
unstable with respect to a two-stream instability in the interface between
these regions. The instability heats the inflowing cold plasma rapidly, on a
timescale comparable to the inverse of its plasma frequency. We then derive
time-independent equations to describe the resulting hot state of the pair
plasma, and describe the conditions under which the spatially uniform solution
is the unique stable solution for the post shock conditions. We also examine
plasmas composed of cold protons and hot electrons, and show that the spatially
uniform solution is the unique stable solution there as well. We state the
shock jump conditions which connect a cold, electron-proton plasma to a hot
electron-proton plasma. The generic feature evident in all of these models is
that the plasma's initial, directed kinetic energy gets almost completely
converted into heat. The magnetic field plays the role of catalyst which can
induce the plasma instability, but our solutions indicate that the macroscopic
field only gets amplified by a factor of approximately three in the frame of
the shock.
