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 Bogomol’nyi bound on the energy is given by two conserved quantities in a similar way that the energy bound for Bogomol’nyi-Prasad-Sommerfield (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 counterparts. We also discuss the underlying [Formula presented] supersymmetry.