Abstract
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.
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