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

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

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.

Keywords: Gross-Pitaevskii equation similarity transformation self-similar solutions

Received: 24 May 2011
Revised: 02 September 2011
Accepted manuscript online:

PACS:	05.45.Yv	(Solitons)
	42.81.Dp	(Propagation, scattering, and losses; solitons)

Fund: 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).

Corresponding Authors: Dai Chao-Qing,dcq424@126.com
E-mail: dcq424@126.com

Cite this article:

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 2012 Chin. Phys. B 21 030508

[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

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

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