On vortices and rings in extended Abelian models

A numerical search for straight superconducting vortices in a U(1) model with a Ginzburg-Landau potential containing a cubic term, is presented. Such vortices exist in a small numerically determined region. The reasons of their existence in that narrow region of the parameter space, as well as of their instability in the rest of the parameter space, are explained. Then, the results of a numerical search for axially symmetric solitons in a U(1)\times U(1) model with higher derivative terms, which is based on Physica D 228 (2007) 159, are presented and discussed.