Exact solutions and localized excitations of (3+1)-dimensional Gross–Pitaevskii system

doi:10.1088/1674-1056/21/7/070304

Abstract Periodic wave solutions and solitary wave solutions to a generalized (3+1)-dimensional Gross--Pitaevskii equation with time-modulated dispersion, nonlinearity, and potential are derived in terms of an improved homogeneous balance principle and a mapping approach. These exact solutions exist under certain conditions via imposing suitable constraints on the functions describing dispersion, nonlinearity, and potential. The dynamics of the derived solutions can be manipulated by prescribing specific time-modulated dispersions, nonlinearities, and potentials. The results show that the periodic waves and solitary waves with novel behaviors are similar to similaritons reported in other nonlinear systems.

Keywords: Gross--Pitaevskii system mapping approach exact solution localized excitation

Received: 16 November 2011
Revised: 05 December 2011
Accepted manuscript online:

PACS:	03.65.Ge	(Solutions of wave equations: bound states)
	05.45.Yv	(Solitons)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11172181), the Natural Science Foundation of Guangdong Province, China (Grant No. 10151200501000008), the Special Foundation of Talent Engineering of Guangdong Province, China (Grant No.2009109), and the Scientific Research Foundation of Key Discipline of Shaoguan University, China (Grant No. ZD2009001).

Corresponding Authors: Zheng Chun-Long
E-mail: zjclzheng@yahoo.com.cn

Cite this article:

Fei Jin-Xi(费金喜) and Zheng Chun-Long(郑春龙) Exact solutions and localized excitations of (3+1)-dimensional Gross–Pitaevskii system 2012 Chin. Phys. B 21 070304

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Exact solutions and localized excitations of (3+1)-dimensional Gross–Pitaevskii system

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