Sound waves and solitons in hot and dense nuclear matter

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.