  The extended Skyrme-Faddeev model possesses vortex solutions in a (3+1)
dimensional Minkowski space-time with target space $CP^N$. They have finite
energy per unit of length and contain waves propagating along vortices with the
speed of light. We introduce various types of the potentials which correspond
with holomorphic solutions of the integrable sector and also with several
numerical solutions outside of this sector. The presented solutions constitute
a strong indication that the current model contains large class of solutions
with much wider range of coupling constants than the previously known exact
solution.
