  Numerical simulations of the NLSE (or GPE) are presented demonstrating
emission of short pulses of the matter (light) density formed in the course of
tunneling in wave-guided light and/or trapped BEC. The phenomenon is observed
under various conditions, for nonlinearities of different signs, zero
nonlinearity included. We study, both numerically and analytically, pulsations
of matter (light) remaining within the trap and use the results in order to
induce emission of sequential pulses by properly narrowing the trap. This
allows us to propose a mechanism for a realization of Atom Pulse Laser.
