Exact Solitonic Solutions of the Gross-Pitaevskii Equation with a Linear Potential

TL;DR

This paper derives exact solitonic solutions for the time-dependent Gross-Pitaevskii equation with a linear potential, revealing a string of bright solitons with specific phase relations and dynamic center of mass behavior.

Contribution

It presents new exact solutions for the Gross-Pitaevskii equation with a linear potential, including the dynamics of soliton strings with phase and motion characteristics.

Findings

String of bright solitons with phase difference of π

Constant relative phase, width, and inter-soliton distance

Center of mass accelerates due to background inhomogeneity

Abstract

We derive classes of exact solitonic solutions of the time-dependent Gross-Pitaevskii equation with repulsive and attractive interatomic interactions. The solutions correspond to a string of bright solitons with phase difference between adjacent solitons equal to $\pi$. While the relative phase, width, and distance between adjacent solitons turn out to be a constant of the motion, the center of mass of the string moves with a constant acceleration arising from the inhomogeneity of the background.