  We theoretically investigate the dynamics of modulation instability (MI) in
two-dimensional spin-orbit coupled Bose-Einstein condensates (BECs). The
analysis is performed for equal densities of pseudo-spin components. Different
combination of the signs of intra- and inter-component interaction strengths
are considered, with a particular emphasize on repulsive interactions. We
observe that the unstable modulation builds from originally miscible
condensates, depending on the combination of the signs of the intra- and
inter-component interaction strengths. The repulsive intra- and inter-component
interactions admit instability and the MI immiscibility condition is no longer
significant. Influence of interaction parameters such as spin-orbit and Rabi
coupling on MI are also investigated. The spin-orbit coupling (SOC) inevitably
contributes to instability regardless of the nature of the interaction. In the
case of attractive interaction, SOC manifest in enhancing the MI. Thus, a
comprehensive study of MI in two-dimensional spin-orbit coupled binary BECs of
pseudo-spin components is presented.
