  We consider a four dimensional field theory with target space being CP^N
which constitutes a generalization of the usual Skyrme-Faddeev model defined on
CP^1. We show that it possesses an integrable sector presenting an infinite
number of local conservation laws, which are associated to the hidden
symmetries of the zero curvature representation of the theory in loop space. We
construct an infinite class of exact solutions for that integrable submodel
where the fields are meromorphic functions of the combinations (x^1+i x^2) and
(x^3+x^0) of the Cartesian coordinates of four dimensional Minkowski
space-time. Among those solutions we have static vortices and also vortices
with waves traveling along them with the speed of light. The energy per unity
of length of the vortices show an interesting and intricate interaction among
the vortices and waves.
