Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows

We use a connection between relativistic hydrodynamics and scalar field theory to generate exact analytic solutions describing non-stationary inhomogeneous flows of the perfect fluid with one-parametric equation of state (EOS) $p=p(\varepsilon)$. For linear EOS $p=\kappa\varepsilon$ we obtain self-similar solutions in the case of plane, cylindrical and spherical symmetries. In the case of extremely stiff EOS ($\kappa=1$) we obtain "monopole $+$ dipole" and "monopole $+$ quadrupole" axially symmetric solutions. We also found some nonlinear EOSs that admit analytic solutions.