Modulational instability for a cubic-quintic model of coupled Gross-Pitaevskii equations with residual nonlinearities

We demonstrate the existence of modulational instability ( MI ) in both trapped miscible and immiscible two component Bose-Einstein condensates. The study is addressed theoretically and numerically in the framework of one-dimensional coupled Gross-Pitaevskii equations incorporating intra- and interspecies cubic-quintic nonlinearities with higher-order ones. Using the time-dependent variational approach, we derive the new Euler-Langrange equations for the time evolution of the phase and amplitude of the modulational perturbation as well as the effective potential and the instability criteria of the system. We examine the effects of higher order nonlinearities on the instability dynamics of the condensates. We show that the modulational properties of the chosen wave numbers are significantly modified. Direct numerical simulations run by the split step Fourier method confirm the analytical predictions.