Detailed investigation of dynamic of Bose-Einstein condensation with two, three body and higher-order interactions

In this study, we investigate the effects of three body and higher-order interactions (HOIs) with two-body interaction on ground state properties of Bose-Einstein condensation (BEC) for combined optical and harmonic potentials in detail by solving new modified Gross-Pitaevskii equation (GPE). In fact, the basis of the study is combinations of attractive and repulsive two-body interaction with other attractive and repulsive interaction types. The obtained results show that taking into account higher order and three-body interactions collectively support to stabilize the BEC system regardless of repulsive or attractive two-body interaction. When repulsive (attractive) binary interaction exists in the system, having at least one attractive (repulsive) interaction type makes the system stable. Also, the stability of the BEC system is discussed by the calculating energy. The energy of the system is determined by semi-analytical approach. Finally, the chemical potential of system is calculated according to different possible combined interaction types. It is observed that generally, the sign of the chemical potential is determined by sign of the strongest interaction in the system, especially three-body interaction. Detailed results are given in this paper.