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We develop numerical tools and apply them to solve the relativisticYang--Mills--Higgs equations in a model where the SU(N) symmetry isspontaneously broken to its center. In SU(2) and SU(3), we obtain the differentfield profiles for infinite and finite center vortices, with endpoints atexternal monopole sources. Exploration of parameter space permits the detectionof a region where the equations get Abelianized. Finally, a generalparametrization of the color structure of SU(2) fields leads us to a referencepoint where an Abelian-like BPS bound is reconciled with N-ality.

Exploring center vortices in SU(2) and SU(3) relativistic Yang-Mills-Higgs models