We derive the leading order radiation through tunneling of an oscillating soliton in a well. We use the hydrodynamic formulation with a rigorous control of the errors for finite times.
We prove for the rescaled convolution map $fto fcircledast f$ propagation of polynomial, exponential and gaussian localization. The gaussian localization is then used to prove an optimal bound on the rate of entropy production by this map. As an appl
ication we prove the convergence of the CLT to be at the optimal rate $1/sqrt{n}$ in the entropy (and $L^1$) sense, for distributions with finite 4th moment.
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 conditio
ns, 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.
