Effect of a potential step or impurity on the Bose-Einstein condensate mean field

TL;DR

This paper analytically derives the stationary states of a one-dimensional Bose-Einstein condensate influenced by a potential step or impurity, revealing novel wavefunctions including asymmetric soliton trains and bound dark solitons.

Contribution

It provides the first closed-form analytic solutions for the mean field states of a BEC with potential steps or impurities, expanding understanding of nonlinear wave behavior.

Findings

Analytic solutions for stationary states in BEC with potential step or impurity

Discovery of asymmetric soliton trains and bound dark solitons

Insight into nonlinear wave phenomena in BEC systems

Abstract

The full set of stationary states of the mean field of a Bose-Einstein condensate in the presence of a potential step or point-like impurity are presented in closed analytic form. The nonlinear Schr\"odinger equation in one dimension is taken as a model. The nonlinear analogs of the continuum of stationary scattering states, as well as evanescent waves, are discussed. The solutions include asymmetric soliton trains and other wavefunctions of novel form, such as a pair of dark solitons bound by an impurity.