New dynamics of the classical and nonlocal Gross-Pitaevskii equation with a parabolic potential
Exactly Solvable and Integrable Systems
2020-12-30 v1 Mathematical Physics
math.MP
Abstract
Solutions of the classical and nonlocal Gross-Pitaevskii (GP) equation with a parabolic potential and a gain term are derived by using a second order nonisospectral Ablowitz-Kaup-Newell-Segur system and reduction technique of double Wronskians. Solutions of the classical GP equation show typical space-time localized characteristics. An interesting dynamics, solitons carrying an oscillating wave, are found with mathematical analysis and illustrations. Solutions of some nonlocal cases are also illustrated.
Keywords
Cite
@article{arxiv.2003.01865,
title = {New dynamics of the classical and nonlocal Gross-Pitaevskii equation with a parabolic potential},
author = {Shi-min Liu and Hua Wu and Da-jun Zhang},
journal= {arXiv preprint arXiv:2003.01865},
year = {2020}
}
Comments
21 pages, 7 figures