Abstract. 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(ε). For linear EOS p = κε we obtain self-similar solutions in the case of plane, cylindrical and spherical symmetries. In the case of extremely stiff EOS (κ = 1) we obtain "monopole + dipole" and "monopole + quadrupole" axially symmetric solutions. We also found some nonlinear EOSs that admit analytic solutions.

We study solutions of the relativistic hydrodynamic equations, which describe spherical or cylindrical expansion of ideal fluid. We derived approximate solutions involving two arbitrary functions which describe the asymptotic behaviour of expanding fireballs in ultra-relativistic limit. In the case of a linear equation of state p(ε) = κε − c1, (0 < κ < 1) we show that the solution may be represented in form of an asymptotic series in negative powers of radial variable; recurrence relations for the coefficients are obtained. This representation is effective if κ > 1/(2J + 1) (J = 2 for spherical expansion and J = 1 for the cylindrical one); in this case the approximate solutions have a wave-like behaviour.

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