Self-gravitating quantum matter may exist in a wide range of cosmological and astrophysical settings from the very early universe through to present-day boson stars. Such arises number different theories, including Peccei-Quinn axion UltraLight (ULDM) or Fuzzy (FDM) dark scenarios. We consider dynamical evolution perturbations spherically symmetric soliton, ground state solution Schr\"{o}dinger...