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 $p = varkapavarepsilon$ we obtain self-similar solutions in the case of plane, cylindrical and spherical symmetries. In the case of extremely stiff EOS ($varkappa = 1$) we obtain ''monopole + dipole'' and ''monopole + quadrupole'' axially symmetric solutions. We also found some nonlinear EOSs that admit analytic solutions.