Solutions of the Schrödinger-Poisson equations for n―dimensional states

We construct stationary solutions for the Schrödinger-Poisson system of equations for n–dimensional states. We find that these have the solitonic profile of the ground state solution of the scalar case n = 1 for all the fields. We numerically study the cases n = 1; 2; 3; 4; 5, because these multifield scenarios have been proposed as a generalization of the scalar field dark matter n = 1, specially vector n = 3 and tensor n = 5 fields. In order to verify the formation of core-halo density profiles we simulate multi-core mergers of equilibrium configurations and show that every field accommodates itself with its own solitonic+halo profie, showing in this way that equilibrium solutions are attractor cores.