Bogomol'nyi equations of Chern-Simons Higgs theory from a generalized abelian Higgs model

We consider a generalization of the abelian Higgs model by introducing a dielectric function and study its Bogomol'nyi limit. The Bogomol'nyi equations of Chern-Simons Higgs theory are obtained as a particular case. We study soliton solutions in the theory and find a criterion under which the theory allows both topological and nontopological solitons. It is also shown that these Bogomol'nyi equations can be obtained through dimensional reduction of four dimensional SU(2) self-dual Yang-Mills equations in a curved space, where the metric itself depends on the gauge potential. (orig.)