Solitons in the Einstein universe
  We show that equations of Newtonian hydrodynamics and gravity with Einstein's
cosmological constant included admit gravitostatic wave solutions propagating
in the background of Einstein's static Universe. In the zero pressure limit
these waves exist at an average matter density exceeding that of Einstein's
Universe. They have the form of a lattice of integrable density singularities
localized at the maxima of the gravitational potential. These singularities are
steady-state counterparts of the so-called Zeldovich pancakes (ZP), interim
wall-like structures appearing at nonlinear stages of development of
gravitational instability. As the average matter density decreases, the period
of the ZP lattice increases diverging at the density of Einstein's Universe.
Solitary wave solutions are found at exactly the density of Einstein's
Universe, and at a slightly larger density the wave may be viewed as a lattice
of well-separated ZP solitons.
