  We show that equations of Newtonian hydrodynamics and gravity describing
one-dimensional steady gas flow possess nonlinear periodic solutions. In the
case of a zero-pressure gas the solution exhibits hydrodynamic similarity and
is universal: it is a lattice of integrable density singularities coinciding
with maxima of the gravitational potential. With finite pressure effects
included, there exists critical matter density that separates two regimes of
behavior. If the average density is below the critical, the solution is a
density wave which is in phase with the wave of the gravitational potential. If
the average density is above the critical, the waves of the density and
potential are out of phase. Traveling plane gravitostatic waves are also
predicted and their properties elucidated. Specifically, subsonic wave is made
out of two out of phase oscillations of matter density and gravitational
potential. If the wave is supersonic, the density-potential oscillations are in
phase.
