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

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

中国物理B ›› 2012, Vol. 21 ›› Issue (7): 70304-070304.doi: 10.1088/1674-1056/21/7/070304

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

费金喜^{a b}, 郑春龙^{a c}

a School of Physics and Electromechanical Engineering, Shaoguan University, Shaoguan 512005, China;
b Faculty of Science, Lishui University, Lishui 323000, China;
c Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

收稿日期:2011-11-16 修回日期:2011-12-05 出版日期:2012-06-01 发布日期:2012-06-01
基金资助:
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).

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

Fei Jin-Xi(费金喜)^a)b) and Zheng Chun-Long(郑春龙)^a)c)†

a School of Physics and Electromechanical Engineering, Shaoguan University, Shaoguan 512005, China;
b Faculty of Science, Lishui University, Lishui 323000, China;
c Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

Received:2011-11-16 Revised:2011-12-05 Online:2012-06-01 Published:2012-06-01
Contact: Zheng Chun-Long E-mail:zjclzheng@yahoo.com.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: Gross--Pitaevskii system, mapping approach, exact solution, localized excitation

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.

Key words: Gross--Pitaevskii system, mapping approach, exact solution, localized excitation

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

05.45.Yv (Solitons)

费金喜, 郑春龙. Exact solutions and localized excitations of (3+1)-dimensional Gross–Pitaevskii system[J]. 中国物理B, 2012, 21(7): 70304-070304.

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[J]. Chin. Phys. B, 2012, 21(7): 70304-070304.

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

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

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