Self-dual Maxwell-Chern-Simons solitons from a Lorentz-violating model

Self-dual abelian Higgs system, involving both the Maxwell and Chern-Simons terms are obtained from Carroll-Field-Jackiw theory by dimensional reduction. Bogomolʼnyi-type equations are studied from theoretical and numerical point of view. In particular, we show that the solutions of these equations are Nielsen-Olesen vortices with electric charge.