The BPS Domain Wall Solutions in Self-Dual Chern-Simons-Higgs Systems

We study domain wall solitons in the relativistic self-dual Chern-Simons Higgs systems by the dimensional reduction method to two dimensional spacetime. The Bogomolny bound on the energy is given by two conserved quantities in a similar way that the energy bound for BPS dyons is set in some Yang-Mills-Higgs systems in four dimensions. We find the explicit soliton configurations which saturate the energy bound and their nonrelativistic counter parts. We also discuss the underlying N=2 supersymmetry.