  We look for topological BPS solutions of an Abelian-Maxwell-Higgs theory
endowed by non-standard kinetic terms to both gauge and scalar fields. Here,
the non-usual dynamics are controlled by two positive functions, G(|{\phi}|)
and w(|{\phi}|), which are related to the self-dual scalar potential
V(|{\phi}|) of the model by a fundamental constraint. The numerical results we
found present interesting new features, and contribute to the development of
the recent issue concerning the study of generalized models and their
applications.
