A numerical study of the Schrodinger-Newton equation 2: the   time-dependent problem
  We present a numerical study of the time-dependent SN equations in 3 dimensions with 3 different kinds of symmetry: spherically symmetric, axially symmetric and translationally symmetric. We find that the solutions manifest the competing tendencies of dispersion from the Schrodinger equation and gravitational attraction from the Poisson equation. Only the ground state is stable, and lumps of probability attract each other gravitationally before dispersing to leave a nugget of the ground state. 
R. Harrison, I. Moroz and K.P. Tod