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We have studied the existence of self-dual effective compact and truecompacton configurations in Abelian Higgs models with generalized dynamics. Wehave named of an effective compact solution the one whose profile behavior isvery similar to the one of a compacton structure but still preserves a tail inits asymptotic decay. In particular we have investigate the electricallyneutral configurations of the Maxwell-Higgs and Born-Infeld-Higgs models andthe electrically charged ones of the Chern-Simons-Higgs andMaxwell-Chern-Simons-Higgs models. The generalization of the kinetic terms isperformed by means of dielectric functions in gauge and Higgs sectors. Theimplementation of the BPS formalism without the need to use a specific\textit{Ansatz} has leaded us to the explicit determination of the dielectricfunction associated to the Higgs sector to be proportional to $\lambda |\phi|^{2\lambda -2}$, $\lambda >1$. Consequently, the followed procedure allows usto determine explicitly new families of self-dual potentials for every model.We have also observed that for sufficiently large values of $\lambda$ everymodel supports effective compact vortices. The true compacton solutions arisingfor $\lambda= \infty $ are analytical. Therefore, this new self-dual structuresenhance the space of BPS solutions of the Abelian Higgs models and theyprobably will imply in interesting applications in physics and mathematics.

Self-dual effective compact and true compacton configurations in generalized Abelian Higgs models