The paper presents a review of results concerning the non-conventional dynamical condensation versus conventional Bose–Einstein condensation, including case generalised van den Berg–Lewis–Pulè condensate. is based on detailed discussion two models: simple toy model and Bogoliubov Weakly Imperfect Bose–Gas model, which was invented for explanation superfluidity liquid $$^{4}{\text{He}}$$ , but a...