  We investigate the density profiles and evolution of weakly self-interacting
cold dark matter haloes using a numerical code based on the collisional
Boltzmann equation. This approach is alternative to N-body techniques in
following the dynamical evolution of haloes in the cosmological context and
taking into account particle self-interaction. The physical case with a cross
section inversely proportional to the relative velocity of the colliding
particles is modelled with an unprecedented resolution, spanning five orders of
magnitude on the radius for each halo. The modelled haloes cover a mass range
from dwarf galaxies to galaxy clusters. We find that for \sigma v_{100} \approx
10^{-24} cm^2/GeV, where \sigma is the cross section per unit mass and v_{100}
is the collision velocity in units of 100 km/s, soft cores in good agreement
with observations on galactic as well as on galaxy cluster scales are obtained.
Remarkably, the observed nearly invariance of the halo central density with
mass is reproduced.
