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

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