Chin. Phys. Lett.  2012, Vol. 29 Issue (7): 070303    DOI: 10.1088/0256-307X/29/7/070303
GENERAL |
Exact Solutions to the Two-Dimensional Spatially Inhomogeneous Cubic-Quintic Nonlinear Schrödinger Equation with an External Potential
CHEN Jun-Chao1, ZHANG Xiao-Fei2,3, LI Biao1**, CHEN Yong4
1Nonlinear Science Center, Ningbo University, Ningbo 315211
2National Time Service Center, Chinese Academy of Sciences, Xi'an 710600
3Institute of Physics, Chinese Academy of Sciences, Beijing 100190
4Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062
Cite this article:   
CHEN Jun-Chao, ZHANG Xiao-Fei, LI Biao et al  2012 Chin. Phys. Lett. 29 070303
Download: PDF(2076KB)  
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

We investigate the two-dimensional spatially inhomogeneous cubic-quintic nonlinear Schrödinger equation with different external potentials. In the absence of external potential or in the presence of harmonic potential, the number of localized nonlinear waves is associated not only with the boundary condition but also with the singularity of inhomogeneous cubic-quintic nonlinearities; while in the presence of periodic external potential, the periodic inhomogeneous cubic-quintic nonlinearities, together with the boundary condition, support the periodic solutions with an arbitrary number of circular rings in every unit. Our results may stimulate new matter waves in high-dimensional Schrödinger equations with spatially modulated nonlinearities.
Received: 19 April 2012      Published: 29 July 2012
PACS:  03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)  
  05.45.Yv (Solitons)  
  02.30.Jr (Partial differential equations)  
  42.65.Tg (Optical solitons; nonlinear guided waves)  
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/10.1088/0256-307X/29/7/070303       OR      https://cpl.iphy.ac.cn/Y2012/V29/I7/070303
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
CHEN Jun-Chao
ZHANG Xiao-Fei
LI Biao
CHEN Yong
[1] Hasegawa A 1989 Optical Solitons in Fibers (Berlin: Springer)
[2] Pitaevski L P and Stringari S 2003 Bose-Einstein Condensation (Oxford: Oxford University)
[3] Davydov A S 1985 Solitons in Molecular Systems (Dordrecht: Reidel)
[4] Malomed B A 2006 Soliton Management in Periodic Systems (Berlin: Springer)
[5] Centurion M et al 2006 Phys. Rev. Lett. 97 033903
[6] Pelinovsky D E et al 2003 Phys. Rev. Lett. 91 240201
[7] Li B et al 2008 Phys. Rev. A 78 023608
[8] Serkin V N et al 2007 Phys. Rev. Lett. 98 074102
[9] Serkin V N et al 2010 Phys. Rev. A 81 023610
[10] Kevrekidis P G et al 2006 J. Phys. A 39 479
[11] Yan J R et al 2012 Chin. Phys. Lett. 29 050302
[12] Cao L J et al 2012 Chin. Phys. Lett. 29 050305
[13] Belmonte-Beitia J et al 2009 J. Phys. A 42 165201
[14] Cardoso W B et al 2011 Phys. Rev. E 83 036604
[15] Wang J M 2011 Chin. Phys. Lett. 28 030202
[16] Liu Y et al 2012 Chin. Phys. Lett. 29 040304
[17] Liu X B et al 2012 Opt. Commun. 285 779
[18] Rodas-Verde M I et al 2005 Phys. Rev. Lett. 95 153903
[19] Carpentier A V 2006 Phys. Rev. A 74 013619
[20] Serkin V N et al 2001 Proc. SPIE 4271 292
[21] Belmonte-Beitia J et al 2007 Phys. Rev. Lett. 98 064102
[22] Tang X Y and Shukla P K 2007 Phys. Rev. A 76 013612
[23] Gao Y et al 2009 Chin. Phys. Lett. 26 030502
[24] Wang D S et al 2010 Phys. Rev. A 81 025604
[25] K?hler T 2002 Phys. Rev. Lett. 89 210404
[26] Boudebs G et al 2003 Opt. Commun. 219 427
[27] Lou S Y et al 1990 Phys. Lett. A 146 45
[28] Clarkson P A et al 1989 J. Math. Phys. 30 2201
[29] Lou S Y et al 2005 J. Phys. A 38 L129
[30] Abramowitz M et al 1965 Handbook of Mathematical Functions (New York: Dover)
[31] Bronski J C et al 2001 Phys. Rev. E 63 036612
Related articles from Frontiers Journals
[1] Haipeng Xue, Lingchii Kong, and Biao Wu. Logarithmic Quantum Time Crystal[J]. Chin. Phys. Lett., 2022, 39(8): 070303
[2] Rong Du, Jian-Chong Xing, Bo Xiong, Jun-Hui Zheng, and Tao Yang. Quench Dynamics of Bose–Einstein Condensates in Boxlike Traps[J]. Chin. Phys. Lett., 2022, 39(7): 070303
[3] Jun-Tao He, Ping-Ping Fang, and Ji Lin. Multi-Type Solitons in Spin-Orbit Coupled Spin-1 Bose–Einstein Condensates[J]. Chin. Phys. Lett., 2022, 39(2): 070303
[4] Peng Gao, Zeyu Wu, Zhan-Ying Yang, and Wen-Li Yang. Reverse Rotation of Ring-Shaped Perturbation on Homogeneous Bose–Einstein Condensates[J]. Chin. Phys. Lett., 2021, 38(9): 070303
[5] Zhao-Long Gu and Jian-Xin Li. Itinerant Topological Magnons in SU(2) Symmetric Topological Hubbard Models with Nearly Flat Electronic Bands[J]. Chin. Phys. Lett., 2021, 38(5): 070303
[6] Hao Li, Chong Liu, Zhan-Ying Yang, Wen-Li Yang. Quantized Superfluid Vortex Filaments Induced by the Axial Flow Effect[J]. Chin. Phys. Lett., 2020, 37(3): 070303
[7] Yu Mo, Cong Zhang, Shiping Feng, Shi-Jie Yang. Solitonic Diffusion of Wavepackets in One-Dimensional Bose–Einstein Condensates[J]. Chin. Phys. Lett., 2019, 36(12): 070303
[8] Jian-Wen Zhou, Xiao-Xun Li, Rui Gao, Wen-Shan Qin, Hao-Hao Jiang, Tao-Tao Li, Ju-Kui Xue. Modulational Instability of Trapped Two-Component Bose–Einstein Condensates[J]. Chin. Phys. Lett., 2019, 36(9): 070303
[9] Shi-Feng Yang, Zi-Tong Xu, Kai Wang, Xiu-Fei Li, Yue-Yang Zhai, Xu-Zong Chen. A Quasi-1D Potential for Bose Gas Phase Fluctuations[J]. Chin. Phys. Lett., 2019, 36(8): 070303
[10] C. Chen, Q. Liu, T. Z. Zhang, D. Li, P. P. Shen, X. L. Dong, Z.-X. Zhao, T. Zhang, D. L. Feng. Quantized Conductance of Majorana Zero Mode in the Vortex of the Topological Superconductor (Li$_{0.84}$Fe$_{0.16}$)OHFeSe[J]. Chin. Phys. Lett., 2019, 36(5): 070303
[11] Bao-Guo Yang, Peng-Ju Tang, Xin-Xin Guo, Xu-Zong Chen, Biao Wu, Xiao-Ji Zhou. Period-Doubled Bloch States in a Bose–Einstein Condensate[J]. Chin. Phys. Lett., 2018, 35(7): 070303
[12] Peng Peng, Liang-Hui Huang, Dong-Hao Li, Zeng-Ming Meng, Peng-Jun Wang, Jing Zhang. Experimental Observation of Spin-Exchange in Ultracold Fermi Gases[J]. Chin. Phys. Lett., 2018, 35(3): 070303
[13] Xu-Dan Chai, Zi-Fa Yu, Ai-Xia Zhang, Ju-Kui Xue. Sound Wave of Spin–Orbit Coupled Bose–Einstein Condensates in Optical Lattice[J]. Chin. Phys. Lett., 2017, 34(9): 070303
[14] Zheng Zhou, Hong-Hua Zhong, Bo Zhu, Fa-Xin Xiao, Ke Zhu, Jin-Tao Tan. Collision Dynamics of Dissipative Matter-Wave Solitons in a Perturbed Optical Lattice[J]. Chin. Phys. Lett., 2016, 33(11): 070303
[15] Yu-E Li, Ju-Kui Xue. Moving Matter-Wave Solitons in Spin–Orbit Coupled Bose–Einstein Condensates[J]. Chin. Phys. Lett., 2016, 33(10): 070303
Viewed
Full text


Abstract

Copyright © Chinese Physics Letters

Address: Institute of Physics, Chinese Academy of Sciences, P. O. Box 603, Beijing 100190 China

Tel: 86-10-82649490, 82649024 Fax: 86-10-82649604 E-mail: cpl@aphy.iphy.ac.cn