Generation of localized patterns in two-component condensates trapped in variable shape optical lattices

Abstract In this work, we discuss the generation of modulational instability in two component Bose-Einstein condensates loaded in deformable shape external optical potentials. As theoretical analysis, we use the time-dependent variational approach which allows us to obtain ordinary differential equations for the time evolution of the amplitude and phase of modulational perturbation. We determine the modulational instability condition by means of effective potential. We show the effects of the optical lattice deformability as well as the cubic and quintic nonlinear interactions on the dynamics of the mixture. Performing direct numerical simulations of the two coupled Gross-Pitaevskii equations (GPEs), we find that our variational and numerical calculations well coincide with each other. The high degree of control on every parameter suggest that our system is relevant for future applications.