Dark solitons and rouge waves for a (2+1)-dimensional Gross–Pitaevskii equation with time-varying trapping potential in the Bose–Einstein condensate. Issue 21 (29th November 2016)

• Record Type: Journal Article
• Authors: Wu, Xiao-Yu; Tian, Bo; Zhen, Hui-Ling; Liu, Lei; Shan, Wen-Rui
• Is Part Of: Journal of modern optics. Volume 63:Issue 21(2016)
• Page Start: 2332
• Page End: 2338
• Publication Date: 2016-11-29
• Subjects: Bose–Einstein condensates -- (2+1)-dimensional Gross–Pitaevskii equation with time-varying trapping potential -- Hirota method -- symbolic computation -- dark solitons -- rouge waves; Optics -- Periodicals; 535
• DOI: 10.1080/09500340.2016.1200683
• Languages: English
• ISSNs: 0950-0340

Abstract

Abstract : Under investigation in this paper is a (2+1)-dimensional Gross–Pitaevskii equation with time-varying trapping potential, which describes the dynamics of the (2+1)-dimensional Bose–Einstein condensate. Employing the Hirota method and symbolic computation, we obtain the dark one-soliton, two-soliton, three-soliton, breather-wave and rouge-wave solutions, respectively. We graphically study the dark solitons with the time-varying harmonic potential and scaled scattering length. Parallel and period solitons are observed. We obtain that when the external trapping potential increases with time, amplitudes of the dark solitons increase and widths of those solitons become narrower; when the external trapping potential is a periodic function, amplitudes and widths of the dark solitons periodically change. Decrease in the scaled scattering length leads to the narrower solitons' widths, but does not affect the solitons' amplitudes. Breather waves and rouge waves are also displayed: Rouge waves emerge when the period of the breather waves go to the infinity.