Variational Analysis of Flat-Top Solitons in Bose–einstein Condensates

Abstract

Static and dynamic properties of matter-wave solitons in dense Bose-Einstein condensates, where three-body interactions play a significant role, have been studied by a variational approximation (VA) and numerical simulations. For experimentally relevant parameters, matter-wave solitons may acquire a flat-top shape, which suggests employing a super-Gaussian trial function for VA. Comparison of the soliton profiles, predicted by VA and those found from numerical solution of the governing Gross-Pitaevskii equation shows good agreement, thereby validating the proposed approach.

Scattering of a flat top solitons of cubic - quintic nonlinear Shrödinger equation by a linear delta potential

“…The main equation we are considering is the one dimensional C-Q NLSE with external potential, and in dimensionless units it can be written in the following form [10] …”

“…U (x) = U 0 δ(x) is the localized external delta potential and further we consider both the potential barrier (U 0 > 0) and well (U 0 < 0) , α and β are, respectively, the coefficients of cubic and quintic nonlinearity. The exact solution of C-Q NLSE (1)with U (x) = 0, in the case of self focusing cubic (α > 0) and defocusing quintic (β > 0) nonlinearity takes the following form [10] ψ(x, t) =…”

“…It should be simple to proceed with analytic calculations and the same time its shape should be close to the solitons form. For flat top soliton this objective can be achieved by the use of super-Gaussian trial function [10]. (1) can be derived from the following Lagrangian density…”

“…As a initial condition we have the flat top soliton with the same parameters as we have used for solution of VE, and the coefficients in C-Q NLSE are also the same [10]. Let us start with the case of weak potential barriers.…”

“…In particular there were evidences that the tunneling through the barrier or quantum reflection and capture on the potential well may happen. In this paper we concentrate on a one type of bright soliton of generalised NLSE, namely the flat top soliton solution of the one dimensinal cubic -quintic NLSE (C-Q NLSE) [12,10]. The C-Q NLSE contains additional term taking into account the higher order, quintic nonlinearity.…”