Numerical and variational solutions of the dipolar Gross-Pitaevskii equation in reduced dimensions

TL;DR

This paper introduces a Gaussian variational method for solving reduced-dimension dipolar Bose-Einstein condensate equations, providing accurate approximations and physical insights into soliton formation.

Contribution

A simple Gaussian variational scheme for reduced quasi-1D and quasi-2D dipolar BEC equations that matches numerical solutions and offers physical understanding.

Findings

Variational scheme agrees well with numerical solutions.

Method provides insights into soliton formation.

Effective for moderate nonlinearities.

Abstract

We suggest a simple Gaussian Lagrangian variational scheme for the reduced time-dependent quasi-one- and quasi-two-dimensional Gross-Pitaevskii (GP) equations of a dipolar Bose-Einstein condensate (BEC) in cigar and disk configurations, respectively. The variational approximation for stationary states and breathing oscillation dynamics in reduced dimensions agrees well with the numerical solution of the GP equation even for moderately large short-range and dipolar nonlinearities. The Lagrangian variational scheme also provides much physical insight about soliton formation in dipolar BEC.