Stabilization of trapless Bose-Einstein condensates without any management

Highlights: • Nonlinear GP equation with two-body, three-body and higher-order interactions is solved by analytical and numerical methods. • So far, both attractive and repulsive trapless BECs have been stabilized by nonlinear managements. • Without management, up to now, there is no model to stabilize the repulsive, trapless BECs at higher dimensions. • We have stabilized the repulsive, trapless BECs without any managements at higher dimensions. -- Abstract: In higher dimensions, so far, both attractive and repulsive trapless Bose-Einstein condensates (BECs) have been stabilized with the help of temporal or spatial management of the two-body contact interaction. However, in the absence of nonlinear management, up to now, there is no model to stabilize the repulsive, trapless BECs at higher dimensions. Hence, in the present study, we tried to stabilize the same and achieved with help of the interplay between three-body and higher-order interactions. In addition, we show that there is an enhancement of the stability of attractive, trapless BECs due to the inclusion of the higher-order interaction along with the two- and three-body interactions. Further, our analytical predictions are corroborated with 4th order Runge-Kutta and split-step Crank-Nicholson numerical results.