Decay of Resonance Structure and Trapping Effect in Potential Scattering Problem of Self-Focusing Wave Packet

TL;DR

This paper numerically investigates how the decay of resonance structures and trapping effects in potential scattering are influenced by nonlinear wave packets governed by the Gross-Pitaevskii equation, focusing on potential width and coupling constants.

Contribution

It provides new insights into the nonlinear scattering behavior of Gaussian wave packets in potential wells, highlighting the roles of coupling constants and potential width.

Findings

Resonance decay depends on potential width and coupling strength.

Transmittance and reflectance are influenced by nonlinear effects.

Behavior differs from linear Schrödinger equation predictions.

Abstract

Potential scattering problems governed by the time-dependent Gross-Pitaevskii equation are investigated numerically for various values of coupling constants. The initial condition is assumed to have the Gaussian-type envelope, which differs from the soliton solution. The potential is chosen to be a box or well type. We estimate the dependences of reflectance and transmittance on the width of the potential and compare these results with those given by the stationary Schr\"odinger equation. We attribute the behaviors of these quantities to the limitation on the width of the nonlinear wave packet. The coupling constant and the width of the potential play an important role in the distribution of the waves appearing in the final state of scattering.