i-SPin: an integrator for multicomponent Schrödinger-Poisson systems with self-interactions

We provide an algorithm and a publicly available code to numerically evolve multicomponent Schr\"{o}dinger-Poisson (SP) systems with SO($n$) symmetry, including attractive or repulsive self-interactions in addition gravity. Focusing on the case where SP system represents non-relativistic limit of massive vector field, non-gravitational (in particular spin-spin interactions) introduce complexities related mass spin conservation which are not present purely gravitational systems. address them analytical solution for `kick' step algorithm, we able decouple completely. Equipped this solution, full field evolution is second order accurate, preserves machine precision, reversible. Our allows expanding universe relevant cosmology, inclusion external potentials laboratory settings.