  The evolution of halos consisting of weakly self-interacting dark matter
particles is investigated using a new numerical Monte-Carlo N-body method. The
halos initially contain kinematically cold, dense 1/r-power-law cores. For
interaction cross sections (sigma/mp) >= 10-100 cm**2/g weak self-interaction
leads to the formation of isothermal, constant density cores within a Hubble
time as a result of heat transfer into the cold inner regions. This core
structure is in good agreement with the observations of dark matter rotation
curves in dwarf galaxies. The isothermal core radii and core densities are a
function of the halo scale radii and scale masses which depend on the
cosmological model. Adopting the currently popular LCDM model, the predicted
core radii and core densities are on good agreement with the observations. For
large interaction cross sections, massive dark halos with scale radii rs >=
14000 cm**2/g/(sigma/mp) kpc could experience core collapse during their
lifetime, leading to cores with singular isothermal density profiles.
