  Analytical and numerical vortex solutions for the extended Skyrme-Faddeev
model in a (3+1) dimensional Minkowski space-time are investigated. The
extension is obtained by adding to the Lagrangian a quartic term, which is the
square of the kinetic term, and a potential which breaks the SO(3) symmetry
down to SO(2). The construction of the solutions has been done in twofold: one
makes use of an axially symmetric ansatz and solves the resulting ODE by an
analytical and a numerical way. The analytical vortices are obtained for
special form of the potentials, and the numerical ones are computed using the
successive over relaxation method for wider choice of the potentials. Another
is based on a simulational technique named the simulated annealing method which
is available to treat the non-axisymmetric shape of solutions. The crucial
thing for determining the structure of vortices is the type of the potential.
