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

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.