“…is the many-body Hamiltonian. This model can describe many phenomena, such as the thermal selfinteraction of beams inside a plasma [37] and the Bose-Einstein condensation (BEC) with magnetic dipole-dipole forces [12], in which the nonlocal interactions are the dipole-dipole interactions between the dilute atoms; consequently, it has been studied in various articles [26,5,33,31,13,36].…”