We show the evolution of non-spherically symmetric balls of a
self-gravitating scalar field in the Newtonian regime or equivalently an ideal
self-gravitating condensed Bose gas. In order to do so, we use a finite
differencing approximation of the Shcr\"odinger-Poisson (SP) system of
equations with axial symmetry in cylindrical coordinates. Our results indicate:
1) that spherically symmetric ground state equilibrium configurations are
stable against non-spherical perturbations and 2) that such configurations of
the SP system are late-time attractors for non-spherically symmetric initial
profiles of the scalar field, which is a generalization of such behavior for
spherically symmetric initial profiles. Our system and the boundary conditions
used, work as a model of scalar field dark matter collapse after the turnaround
point. In such case, we have found that the scalar field overdensities tolerate
non-spherical contributions to the profile of the initial fluctuation.Comment: 8 revtex pages, 10 eps figures. Accepted for publication in PR