  An alternative approach to solving the Landau-Khalatnikov problem on
one-dimensional stage of expansion of hot hadronic matter created in collisions
of high-energy particles or nuclei is suggested. Solving the relativistic
hydrodynamics equations by the Riemann method yields a representation for
Khalatnikov's potential which satisfies explicitly the condition of symmetry of
the matter flow with respect to reflection in the central plane of the initial
distribution of matter. New exact relationships are obtained for evolution of
the density of energy in the center of the distribution and for laws of motion
of boundaries between the general solution and the rarefaction waves. The
rapidity distributions are derived in the Landau approximation with account of
the pre-exponential factor.
