Stability analysis of 3D cubic-quintic Gross–Pitaevskii equation with elastic and inelastic collisions

In this paper, we study the stability of three-dimensional Bose–Einstein condensates of finite temperatures at which both elastic and inelastic collisions are taken into account. The modeled governing Gross–Pitaevskii equation reveals inclusion of both real and imaginary components in the nonlinear terms. We find the stability region for a wide range of two- and three-body interaction terms with the inclusion of both gain and loss effects by using the Jacobian matrix. We investigate the stability of the system for possible different states of those cases. The stability properties of three-dimensional condensates are strongly altered by tuning the gain rate of their elastic collisions. These strong losses impose severe limitations for using Feshbach resonances. We finally sustain our semi-analytical findings with the results of inclusive numerical simulations.