  We demonstrate the existence of compactons matter waves in binary mixtures of
Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) subjected
to equal contributions of intra-species Rashba and Dresselhaus spin-orbit
coupling (SOC) under periodic time modulations of the intra-species scattering
length. We show that these modulations lead to the rescaling of the SOC
parameters that involve the density imbalance of the two components. This gives
rise to a density-dependent SOC parameters strongly influence the existence and
stability of compacton matter waves. The stability of SOC-compactons is
investigated both by linear stability analysis and by time integrations of the
coupled Gross-Pitaevskii equations. We find that SOC restricts the parameter
ranges for stable stationary SOC-compacton existence but, on the other side, it
gives a more stringent signature of their occurrence. In particular,
SOC-compactons should appear when the intra-species interactions and the number
of atoms in the two components are perfectly balanced (or close to being
balanced for metastable cases). The possibility to use SOC-compactons as a tool
for indirect measurements of the number of atoms and/or the intra-species
interactions, is also suggested.
