Quantum corrections to the modulational instability of Bose-Einstein condensates with two- and three-body interactions

We study the amplitude perturbations of the cubic-quintic Gross-Piteavskii equation for weakly trapped Bose-Einstein condensates through a semiquantum procedure. After a quantization of the original problem, with the introduction of quantum degrees of freedom as the fluctuations around classical parameters, a new dynamical modulational instability condition is derived. Corrective terms bear quantum effects that play a crucial role over the reshape of instability domain and sometimes train all unstable modes into full stability. By making use of several indicators through direct numerical simulations of the subsequent set of equations of motion, we found that there are rooms of regular trajectories and those of totally chaotic ones that are strictly related to instability. These numerical results are in agreement with the analytical predictions regarding the stabilization of Bose-Einstein condensates.