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We study vortex solutions in the Born-Infeld theory coupled with a complexscalar field. We show that for a specific form of the "Higgs" potential thevortex satisfies a set of Bogomol'nyi-type equations. Another model, withnonlinear interaction between gauge and Higgs fields, is also considered. Weshow how it is derived from a supersymmetric extension of the Born-Infeldtheory with a minimally coupled complex scalar field.

Bogomol'nyi Equations for Vortices in Born-Infeld-Higgs Systems