We construct self-dual Born–Infeld vortices induced from a generalized Higgs mechanism. Two specific models of the theory are of focused interest where the Higgs potential is either of a |ϕ|4- or |ϕ|6-type. For the |ϕ|4-model, we obtain a sharp existence and uniqueness theorem for doubly periodic and planar vortices. For doubly periodic solutions, a necessary and sufficient condition for the existence is explicitly derived in terms of the vortex number, the Born–Infeld parameter, and the size of the periodic lattice domain. For the |ϕ|6-model, we show that both topological and non-topological vortices are present. This new phenomenon distinguishes the model from the classical Born–Infeld–Higgs theory studied earlier in the literature. A series of results regarding doubly periodic, topological, and non-topological vortices in the |ϕ|6-model are also established.
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