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We consider a four dimensional field theory with target space being CP^Nwhich constitutes a generalization of the usual Skyrme-Faddeev model defined onCP^1. We show that it possesses an integrable sector presenting an infinitenumber of local conservation laws, which are associated to the hiddensymmetries of the zero curvature representation of the theory in loop space. Weconstruct an infinite class of exact solutions for that integrable submodelwhere 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 Minkowskispace-time. Among those solutions we have static vortices and also vorticeswith waves traveling along them with the speed of light. The energy per unityof length of the vortices show an interesting and intricate interaction amongthe vortices and waves.

Exact vortex solutions in a CP^N Skyrme-Faddeev type model