  We construct analytical and numerical vortex solutions for an extended
Skyrme-Faddeev model in a $(3+1)$ dimensional Minkowski space-time. 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 makes use of an ansatz, invariant under the
joint action of the internal SO(2) and three commuting U(1) subgroups of the
Poincar\'e group, and which reduces the equations of motion to an ODE for a
profile function depending on the distance to the $x^3$-axis. The vortices have
finite energy per unit length, and have waves propagating along them with the
speed of light. The analytical vortices are obtained for special choice of
potentials, and the numerical ones are constructed using the Successive Over
Relaxation method for more general potentials. The spectrum of solutions is
analyzed in detail, specially its dependence upon special combinations of
coupling constants.
