Bogomol'nyi limit for nontopological solitons in a Chern-Simons model with anomalous magnetic moment

We study an Abelian Chern-Simons (CS) model which includes both the CS term and an anomalous magnetic contribution. We find that, for a special relation between the CS mass and the anomalous magnetic coupling, the equations for the gauge fields reduce from second- to first-order differential equations. It is shown that charged vortices of finite energy exist. Furthermore, we show that nontopological solitons satisfy a set of Bogomol'nyi-type equations for a simple (m2/2)φ2 potential, when m and the topological mass are equal