  We study the domain wall soliton solutions in the relativistic self-dual
Maxwell Chern-Simons model in 1+1 dimensions obtained by the dimensional
reduction of the 2+1 model. Both topological and nontopological self-dual
solutions are found in this case. A la BPS dyons here the Bogomol'ny bound on
the energy is expressed in terms of two conserved quantities. We discuss the
underlying supersymmetry. Nonrelativistic limit of this model is also
considered and static, nonrelativistic self-dual soliton solutions are
obtained.
