Abstract
We consider two self-dual abelian Higgs systems obtained from Lorentz breaking symmetry models by dimensional reduction. For the first model, we show that the self-dual equations are identical to those of Nielsen-Olesen vortices. Also, we show that our vortices have electric charge. In the second case we show that self-dual Chern-Simons-Higgs vortices without electric charge are possible.
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