Spatiotemporal self-similar solutions for the nonautonomous (3+1)-dimensional cubic–quintic Gross–Pitaevskii equation

doi:10.1088/1674-1056/21/3/030508

中国物理B ›› 2012, Vol. 21 ›› Issue (3): 30508-030508.doi: 10.1088/1674-1056/21/3/030508

戴朝卿,陈瑞品,王悦悦

收稿日期:2011-05-24 修回日期:2011-09-02 出版日期:2012-02-15 发布日期:2012-02-15
通讯作者: 戴朝卿,dcq424@126.com E-mail:dcq424@126.com

Spatiotemporal self-similar solutions for the nonautonomous (3+1)-dimensional cubic–quintic Gross–Pitaevskii equation

Dai Chao-Qing(戴朝卿)^†, Chen Rui-Pin(陈瑞品), and Wang Yue-Yue(王悦悦)

School of Sciences, Zhejiang Agricultural and Forestry University, Linán 311300, China

Received:2011-05-24 Revised:2011-09-02 Online:2012-02-15 Published:2012-02-15
Contact: Dai Chao-Qing,dcq424@126.com E-mail:dcq424@126.com
Supported by:
Project supported by the National Natural Science Foundations of China (Grant No. 11005092), the Program for Innovative Research Team of Young Teachers (Grant No. 2009RC01), and the Scientific Research and Developed Fund of Zhejiang Agricultural and Forestry University, China (Grant No. 2009FK42).

摘要/Abstract

Abstract: With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous (3+1)-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction, nonlinearity, harmonic potential and gain or loss when two constraints are satisfied. These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction, nonlinearity and the gain/loss. Based on these analytical results, we investigate the dynamic behaviours in a periodic distributed amplification system.

Key words: Gross-Pitaevskii equation, similarity transformation, self-similar solutions

中图分类号: (Solitons)

05.45.Yv

42.81.Dp (Propagation, scattering, and losses; solitons)

戴朝卿,陈瑞品,王悦悦. [J]. 中国物理B, 2012, 21(3): 30508-030508.

Dai Chao-Qing(戴朝卿), Chen Rui-Pin(陈瑞品), and Wang Yue-Yue(王悦悦) . Spatiotemporal self-similar solutions for the nonautonomous (3+1)-dimensional cubic–quintic Gross–Pitaevskii equation[J]. Chin. Phys. B, 2012, 21(3): 30508-030508.

参考文献 20

[1]	Dai C Q and Zhang J F 2005 Int. Mod. Phys. B 19 2129
[2]	Liu S K, Zhao Q and Liu S D 2011 Chin. Phys. B 20 040202
[3]	Yang Z, Ma S H and Fang J P 2011 Chin. Phys. B 20 040301
[4]	Yang Z, Ma S H and Fang J P 2011 Chin. Phys. B 20 060506
[5]	Dai C Q and Zhang J F 2006 Opt. Commun. 263 309
[6]	Li B Q, Ma Y L, Wang C, Xu M P and Li Y 2011 Acta Phys. Sin. 60 060203 (in Chinese)
[7]	Wang H and Li B 2011 Chin. Phys. B 20 040203
[8]	Qian C, Wang L L and Zhang J F 2011 Acta Phys. Sin. 60 064214 (in Chinese)
[9]	Dai C Q, Wang Y Y and Yan C J 2010 Opt. Commun. 283 1489
[10]	Zong F D, Yang Y and Zhang J F 2011 Acta Phys. Sin. 60 3670 (in Chinese)
[11]	Sulem C and Sulem P 2000 The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse (Berlin: Springer-Verlag)
[12]	Adhikari S K 2004 Phys. Rev. A 69 063613
[13]	Saito H and Ueda M 2003 Phys. Rev. Lett. 90 040403
[14]	Dai C Q, Wang Y Y and Zhang J F 2010 Opt. Lett. 35 1437
[15]	Dai C Q, Chen R P and Zhou G Q 2011 J. Phys. B: At. Mol. Opt. Phys. 44 145401
[16]	Dai C Q, Wang D S, Wang L L, Zhang J F and Liu W M 2011 Ann. Phys. 326 2356
[17]	Zhang W X, She Y C and Wang D L 2011 Acta Phys. Sin. 60 070514 (in Chinese)
[18]	Abdullaev F K, Gammal A, Tomio L and Frederico T 2001 Phys. Rev. A 63 043604
[19]	Jiang L H and Wu H Y 2011 Opt. Commun. 284 2022
[20]	Yang R C, Hao R Y, Li L, Shi X J, Li Z H and Zhou G S 2005 Opt. Commun. 253 177

Spatiotemporal self-similar solutions for the nonautonomous (3+1)-dimensional cubic–quintic Gross–Pitaevskii equation

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 20

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Wei Qi(漆伟), Xiao-Gang Guo(郭晓刚), Liang-Wei Dong(董亮伟), and Xiao-Fei Zhang(张晓斐). Modulational instability of a resonantly polariton condensate in discrete lattices[J]. 中国物理B, 2023, 32(3): 30502-030502.
[2]	Shubin Wang(王树斌), Xin Zhang(张鑫), Guoli Ma(马国利), and Daiyin Zhu(朱岱寅). All-optical switches based on three-soliton inelastic interaction and its application in optical communication systems[J]. 中国物理B, 2023, 32(3): 30506-030506.
[3]	Yiyuan Zhang(张艺源), Ziqi Liu(刘子琪), Jiaxin Qi(齐家馨), and Hongli An(安红利). Soliton molecules, T-breather molecules and some interaction solutions in the (2+1)-dimensional generalized KDKK equation[J]. 中国物理B, 2023, 32(3): 30505-030505.
[4]	Wen-Xiu Ma(马文秀). Matrix integrable fifth-order mKdV equations and their soliton solutions[J]. 中国物理B, 2023, 32(2): 20201-020201.
[5]	Nkeh Oma Nfor, Patrick Guemkam Ghomsi, and Francois Marie Moukam Kakmeni. Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane[J]. 中国物理B, 2023, 32(2): 20504-020504.
[6]	Xuefeng Zhang(张雪峰), Tao Xu(许韬), Min Li(李敏), and Yue Meng(孟悦). Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation[J]. 中国物理B, 2023, 32(1): 10505-010505.
[7]	D Chevizovich, S Zdravković, A V Chizhov, and Z Ivić. Charge self-trapping in two strand biomolecules: Adiabatic polaron approach[J]. 中国物理B, 2023, 32(1): 10506-010506.
[8]	Jing Wang(王静), Hua Wu(吴华), and Da-Jun Zhang(张大军). Reciprocal transformations of the space-time shifted nonlocal short pulse equations[J]. 中国物理B, 2022, 31(12): 120201-120201.
[9]	Guofei Zhang(张国飞), Jingsong He(贺劲松), and Yi Cheng(程艺). Riemann-Hilbert approach and N double-pole solutions for a nonlinear Schrödinger-type equation[J]. 中国物理B, 2022, 31(11): 110201-110201.
[10]	Jing Wang(王静), Xue-Li Ding(丁学利), and Biao Li(李彪). Fusionable and fissionable waves of (2+1)-dimensional shallow water wave equation[J]. 中国物理B, 2022, 31(10): 100502-100502.
[11]	Shu-Wen Guan(关淑文), Ling-Zheng Meng(孟令正), and Li-Chen Zhao(赵立臣). Oscillation properties of matter-wave bright solitons in harmonic potentials[J]. 中国物理B, 2022, 31(8): 80506-080506.
[12]	Denghui Li(李登慧), Fei Wang(王菲), and Zhaowen Yan(颜昭雯). Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters[J]. 中国物理B, 2022, 31(8): 80202-080202.
[13]	Hong-Cai Ma(马红彩), Yi-Dan Gao(高一丹), and Ai-Ping Deng(邓爱平). Solutions of novel soliton molecules and their interactions of (2 + 1)-dimensional potential Boiti-Leon-Manna-Pempinelli equation[J]. 中国物理B, 2022, 31(7): 70201-070201.
[14]	Ahmet Bekir and Emad H M Zahran. Nonlinear dynamical wave structures of Zoomeron equation for population models[J]. 中国物理B, 2022, 31(6): 60401-060401.
[15]	Xi-zhong Liu(刘希忠) and Jun Yu(俞军). A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis[J]. 中国物理B, 2022, 31(5): 50201-050201.