  We investigate vortex soliton solutions in 2+1 dimensional scalar gauge
theories, in the presence of source terms in the action. Concretely, this would
be applied to anyons, as well as the Fractional Quantum Hall Effect (FQHE). We
classify solitons for renormalizable potentials, as well as some
nonrenormalizable examples that could be relevant for the FQHE. The non-Abelian
case, specifically for theories with global non-Abelian symmetries, is also
investigated, as is the non-relativistic limit of the above theories, when we
get a modification of the Jackiw-Pi model, with an interesting new vortex
solution. We explore the application to the ABJM model, as well as more general
SYM-CS models in 2+1 dimensions.
