Exact Solitonic Solutions of the One-Dimensional Gross-Pitaevskii Equation with a Time-Dependent Harmonic Potential and Interatomic Interaction

TL;DR

This paper derives exact solitonic solutions for the one-dimensional Gross-Pitaevskii equation with time-varying harmonic potential and interatomic interactions, enabling control over soliton dynamics and trapping.

Contribution

It presents a method to obtain exact solutions for a time-dependent Gross-Pitaevskii equation with variable potential and interactions, advancing understanding of soliton control.

Findings

Solutions describe breathing single and multiple solitons.

External potential oscillations control soliton center dynamics.

Solitons can be trapped at the potential center under certain conditions.

Abstract

We derive exact solitonic solutions of the one-dimensional time-dependent Gross-Pitaevskii equation with time-dependent strengths of the harmonic external potential and the interatomic interaction. The time-dependence of the external potential and interatomic interaction are given in terms of a general function of time. For an oscillating strength of the external potential, the solutions correspond to breathing single and multiple solitons. The amplitude and frequency of the oscillating potential can be used to control the dynamics of the center of mass of the solitons. For certain values of these parameters, the solitons can be {\it trapped} at the center of the harmonic potential.