Exact solitonic solutions of the Gross-Pitaevskii equation with a linear potential.
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.
Physics Department, United Arab Emirates University, P.O. Box 17551, Al-Ain, United Arab Emirates.
Usama
U
Al Khawaja