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In this paper, we investigate the impact of higher-order interactions on themodulational instability (MI) of Bose-Einstein Condensates (BECs) immersed inan optical lattice potential. We derive the new variational equations for thetime evolution of amplitude, phase of modulational perturbation, and effectivepotential for the system. Through effective potential techniques, we find thathigh density attractive and repulsive BECs exhibit new character with directimpact over the MI phenomenon. Results of intensive numerical investigationsare presented and their convergence with the above semi analytical approach isbrought out.

Role of higher-order interactions on the modulational instability of Bose-Einstein condensate trapped in a periodic optical lattice