Phases of the Bose-Einstein condensate dark matter model with both two-
  and three-particle interactions
  In this paper we further elaborate on the Bose-Einstein condensate (BEC) dark
matter model extended in our preceding work [Phys. Rev. D 102, 083510 (2020)]
by the inclusion of 6th order (or three-particle) repulsive self-interaction
term. Herein, our goal is to complete the picture through adding to the model
the 4th order repulsive self-interaction. The results of our analysis confirm
the following: while in the preceding work the two-phase structure and the
possibility of first-order phase transition was established, here we
demonstrate that with the two self-interactions involved, the nontrivial phase
structure of the enriched model remains intact. For this to hold, we study the
conditions which the parameters of the model, including the interaction
parameters, should satisfy. As a by-product and in order to provide some
illustration, we obtain the rotation curves and the (bipartite) entanglement
entropy for the case of particular dwarf galaxy.
