  Assuming that nuclear matter can be treated as a perfect fluid, we study the
propagation of perturbations in the baryon density. The equation of state is
derived from a relativistic mean field model, which is a variant of the
non-linear Walecka model. The expansion of the Euler and continuity equations
of relativistic hydrodynamics around equilibrium configurations leads to
differential equations for the density fluctuations. We solve them numerically
for linear and spherical perturbations and follow the time evolution of the
initial pulses. For linear perturbations we find single soliton solutions and
solutions with one or more solitons followed by radiation. Depending on the
equation of state a strong damping may occur. Spherical perturbations are
strongly damped and almost do not propagate. We study these equations also for
matter at finite temperature. Finally we consider the limiting case of shock
wave formation.
