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For the study of topological vortices with non-minimal coupling, we built a kind of non-canonical O(3)-sigma model, with a Maxwell term modified by a dielectric function. Through the BPS formalism an investigation is made on possible configurations of vortices in topological sectors of the sigma model and the real scalar field. For a particular ansatz, the solutions of the topological sector of the real scalar field are described by the known kink solutions. On the other hand, when studying the vortices in non-minimal sector of the pure O(3)-sigma model, it is detected the emergence of solutions that generate solitary waves similar to structures derived from a KdV-like theory. We observed that in the study of mixed models, namely, the topological sector of the O(3)-sigma model coupled to the topological sector of the real scalar field, the vortex solutions assume a profile of a step function. Then, when kinks of the topological sector of the scalar field are interacting with the field of the sigma model, it makes the field solutions of the O(3)-sigma model become extremely localized, making the vortice structures non-physical.