One-dimension cubic-quintic Gross-Pitaevskii equation in Bose-Einstein condensates in a trap potential

TL;DR

This paper introduces a new variational method to solve the 1D cubic-quintic Gross-Pitaevskii equation in Bose-Einstein condensates, analyzing the effects of transversal motion and providing error estimates for simpler models.

Contribution

It presents a direct analytical solution for the 1D cubic-quintic GPE with a harmonic trap, incorporating transversal effects and error analysis for cubic-only approximations.

Findings

Derived a closed-form solution for the cubic-quintic GPE.

Quantified the impact of transversal motion on 1D BEC models.

Provided an error estimate for cubic-only GPE descriptions.

Abstract

By means of new general variational method we report a direct solution for the quintic self-focusing nonlinearity and cubic-quintic 1D Gross Pitaeskii equation (GPE) in a harmonic confined potential. We explore the influence of the 3D transversal motion generating a quintic nonlinear term on the ideal 1D pure cigar-like shape model for the attractive and repulsive atom-atom interaction in Bose Einstein condensates (BEC). Also, we offer a closed analytical expression for the evaluation of the error produced when solely the cubic nonlinear GPE is considered for the description of 1D BEC.