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We use a connection between relativistic hydrodynamics and scalar fieldtheory to generate exact analytic solutions describing non-stationaryinhomogeneous flows of the perfect fluid with one-parametric equation of state(EOS) $p = p(\epsilon)$. For linear EOS $p = \kappa \epsilon$ we obtainself-similar solutions in the case of plane, cylindrical and sphericalsymmetries. In the case of extremely stiff EOS ($\kappa=1$) we obtain''monopole + dipole'' and ''monopole + quadrupole'' axially symmetricsolutions. We also found some nonlinear EOSs that admit analytic solutions.

Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows