The extended Skyrme–Faddeev model possesses vortex solutions in a ($3+1$)-dimensional Minkowski space-time with target space $C{P}^N$. They have finite energy per unit of length and contain waves propagating along the 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 a large class of solutions with a wide range of coupling constants, and the exact solution is just a particular case.

• Received 10 April 2015

DOI:https://doi.org/10.1103/PhysRevD.92.045007