Exact analytical solutions of three-dimensional Gross–Pitaevskii equation with time–space modulation

doi:10.1088/1674-1056/20/5/050315

Abstract By the generalized sub-equation expansion method and symbolic computation, this paper investigates the (3+1)-dimensional Gross–Pitaevskii equation with time- and space-dependent potential, time-dependent nonlinearity, and gain or loss. As a result, rich exact analytical solutions are obtained, which include bright and dark solitons, Jacobi elliptic function solutions and Weierstrass elliptic function solutions. With computer simulation, the main evolution features of some of these solutions are shown by some figures. Nonlinear dynamics of a soliton pulse is also investigated under the different regimes of soliton management.

Keywords: Gross–Pitaevskii equation soliton solutions Bose–Einstein condensate symbolic computation

Received: 23 November 2010
Revised: 23 December 2010
Accepted manuscript online:

PACS:	03.75.-b
	05.45.Yv	(Solitons)
	31.15.-p	(Calculations and mathematical techniques in atomic and molecular physics)

Fund: Project supported by Zhejiang Provincial Natural Science Foundations of China (Grant No. Y6090592), National Natural Science Foundation of China (Grant Nos. 11041003 and 10735030), Ningbo Natural Science Foundation (Grant Nos. 2010A610095, 2010A610103, and 2009B21003), and K.C. Wong Magna Fund in Ningbo University of China.

Cite this article:

Hu Xiao(胡晓) and Li Biao(李彪) Exact analytical solutions of three-dimensional Gross–Pitaevskii equation with time–space modulation 2011 Chin. Phys. B 20 050315

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Exact analytical solutions of three-dimensional Gross–Pitaevskii equation with time–space modulation

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