  Binary mixtures of quasi one-dimensional Bose-Einstein condensates (BEC)
trapped in deep optical lattices (OL) in the presence of periodic time
modulations of the inter-species scattering length, are investigated. We adopt
a mean field description and use the tight binding approximation and the
averaging method to derive averaged model equations in the form of two coupled
discrete nonlinear Schr\"odinger equations (DNLSE) with tunneling constants
that nonlinearly depend on the inter-species coupling. We show that for strong
and rapid modulations of the inter-species scattering length, the averaged
system admits exact compacton solutions, e.g. solutions that have no tails and
are fully localized on a compact which are achieved when the densities at the
compact edges are in correspondence with zeros of the Bessel function (zero
tunneling condition). Deviations from exact conditions give rise to the
formation of quasi-compactons, e.g. non exact excitations which look as
compactons for any practical purpose, for which the zero tunneling condition is
achieved dynamically thanks to an effective nonlinear dispersive coupling
induced by the scattering length modulation. Stability properties of compactons
and quasi-compactons are investigated by linear analysis and by numerical
integrations of the averaged system, respectively, and results compared with
those from the original (unaveraged) system. In particular, the occurrence od
delocalizing transitions with existence of thresholds in the mean inter-species
scattering length is explicitly demonstrated. Under proper management
conditions, stationary compactons and quasi-compactons are quite stable and
robust excitations that can survive on very long time scale. A parameter design
and a possible experimental setting for observation of these excitations are
briefly discussed.
