Note on generalization of Jackiw-Pi Vortices

We analyze two abelian Higgs systems with nonstandard kinetic terms. We consider a model involving the Maxwell term. For a particular choice of the nonstandard kinetics, we are able to obtain generalized Jackiw-Pi vortices. We, also, analyze a generalization of the Jackiw-Pi model. In that case we show that the system support the Nielsen-Olesen vortices as solutions.