Eur. Phys. J. D (2013) 67: 143
https://doi.org/10.1140/epjd/e2013-40163-9

Regular Article

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

¹ Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil
² Universidade Federal do Rio de Janeiro, C.P. 68530, Rio de Janeiro, Brazil
³ Mediterranean Institute of Fundamental Physics, Via Appia Nuova 31, 00040 Rome, Italy

^a e-mail: cipolatti@im.ufrj.br

Received: 24 September 2012
Received in final form: 14 April 2013
Published online: 16 July 2013

Abstract

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