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 Khalatnikovs 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.
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