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

3-3-1 Self Interacting Dark Matter and the Galaxy Core-Cusp problem