Dynamics of matter-wave solutions of Bose-Einstein condensates in a homogeneous gravitational field

TL;DR

This paper derives and analyzes matter-wave solutions, including bright and dark solitons, for Bose-Einstein condensates in a harmonic trap under gravity, highlighting control via scattering length adjustments.

Contribution

It introduces a method to generate and manipulate matter-wave solutions in gravitational fields by controlling the scattering length.

Findings

Solutions include bright and dark solitons.

Gravity influences the dynamics and kinematics of solutions.

Manipulation of solutions is possible without altering gravitational or magnetic fields.

Abstract

We find a matter-wave solution of Bose-Einstein condensates trapped in a harmonic-oscillator potential and subjected to a homogeneous gravitational field, by means of the extended tanhfunction method. This solution has as special cases the bright and dark solitons. We investigate the dynamics and the kinematics of these solutions, and the role of gravity is sketched. It is shown that these solutions can be generated and manipulated by controlling the s-wave scattering length, without changing the strengths of the magnetic and gravitational fields.