  In this paper, we investigate the impact of higher-order interactions on the
modulational instability (MI) of Bose-Einstein Condensates (BECs) immersed in
an optical lattice potential. We derive the new variational equations for the
time evolution of amplitude, phase of modulational perturbation, and effective
potential for the system. Through effective potential techniques, we find that
high density attractive and repulsive BECs exhibit new character with direct
impact over the MI phenomenon. Results of intensive numerical investigations
are presented and their convergence with the above semi analytical approach is
brought out.
