We develop numerical tools and apply them to solve the relativistic Yang--Mills--Higgs equations in a model where the SU(N) symmetry is spontaneously broken to its center. In SU(2) and SU(3), we obtain the different field profiles for infinite and finite center vortices, with endpoints at external monopole sources. Exploration of parameter space permits the detection of a region where the equations get Abelianized. Finally, a general parametrization of the color structure of SU(2) fields leads us to a reference point where an Abelian-like BPS bound is reconciled with N-ality.
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