  The core-cusp problem remains as a challenging discrepancy between
observations and simulations in the standard $\Lambda$CDM model for the
formation of galaxies. The problem is that $\Lambda$CDM simulations predict a
steep power-law mass density profile at the center of galactic dark matter
halos. However, observations of dwarf galaxies in the Local Group reveal a
density profile consistent with a nearly flat distribution of dark matter near
the center. A number of solutions to this dilemma have been proposed. Here, we
summarize investigations into the possibility that the dark matter particles
themselves self interact and scatter. Such self-interacting dark matter (SIDM)
particles can smooth out the dark-matter profile in high-density regions. We
also review the theoretical proposal that self-interacting dark matter may
arise as an additional Higgs scalar in the 3-3-1 extension of the standard
model. We present new simulations of galaxy formation and evolution for this
formulation of self-interacting dark matter. Current constraints on this
self-interacting dark matter are then summarized.
