Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

doi:10.1088/1674-1056/20/11/114219

中国物理B ›› 2011, Vol. 20 ›› Issue (11): 114219-114219.doi: 10.1088/1674-1056/20/11/114219

Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

刘晓蓓, 李彪

Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China

收稿日期:2011-04-11 修回日期:2011-05-26 出版日期:2011-11-15 发布日期:2011-11-15
基金资助:
Project supported by the Zhejiang Provincial Natural Science Foundations, China (Grant No. Y6090592), the National Natural Science Foundation of China (Grant Nos. 11041003 and 10735030), the Ningbo Natural Science Foundation, China (Grant Nos. 2010A610095, 2010A610103, and 2009B21003), and K.C. Wong Magna Fund in Ningbo University, China.

Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

Liu Xiao-Bei(刘晓蓓) and Li Biao(李彪)^†

Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China

Received:2011-04-11 Revised:2011-05-26 Online:2011-11-15 Published:2011-11-15
Supported by:
Project supported by the Zhejiang Provincial Natural Science Foundations, China (Grant No. Y6090592), the National Natural Science Foundation of China (Grant Nos. 11041003 and 10735030), the Ningbo Natural Science Foundation, China (Grant Nos. 2010A610095, 2010A610103, and 2009B21003), and K.C. Wong Magna Fund in Ningbo University, China.

摘要/Abstract

摘要： We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters. Different shapes of bright solitons, a train of bright solitons and dark solitons are observed. The obtained results may raise the possibilities of relevant experiments and potential applications.

关键词: (3+1)-dimensional nonlinear Schö, dinger Equation, optical soliton, soliton propagation

Abstract: We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters. Different shapes of bright solitons, a train of bright solitons and dark solitons are observed. The obtained results may raise the possibilities of relevant experiments and potential applications.

Key words: (3+1)-dimensional nonlinear Sch?dinger Equation, optical soliton, soliton propagation

中图分类号: (Propagation, scattering, and losses; solitons)

42.81.Dp

02.30.Jr (Partial differential equations) 05.45.Yv (Solitons)

刘晓蓓, 李彪. Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients[J]. 中国物理B, 2011, 20(11): 114219-114219.

Liu Xiao-Bei(刘晓蓓) and Li Biao(李彪) . Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients[J]. Chin. Phys. B, 2011, 20(11): 114219-114219.

参考文献 42

[1]	Zabusky N J and Kruskal M D 1965 Phys. Rev. Lett. 15 240
[2]	Drazin P G and Johnson R S 1996 Solitons: an Introduction (Cambridge: Cambridge University Press)
[3]	Ablowitz M J and Clarkson P A 1991 Soliton, Nonlinear Evolution Equations and Inverse Scattering (New York: Cambridge University Press)
[4]	Gu C H, Hu H S and Zhou Z X 1999 Darboux Transformation in Soliton Theory and Its Geometric Applications (Shanghai: Shanghai Scientific and Technical Press) (in Chinese)
[5]	Hirota R 2004 The Direct Method in Soliton Theory (Cambridge: Cambridge University Press)
[6]	Wazwaz A M 2009 Partial Differential Equations and Solitary Waves Theory (Springer: High Education Press)
[7]	Adomian G 1994 Solving Frontier Problems of Physics: The Decomposition Method (Boston: Kluwer Academic Publishers)
[8]	Li Z B and Liu Y P 2002 Comput. Phys. Commun. 148 256
[9]	Fan E 2000 Phys. Lett. A 277 212
[10]	Li B, Chen Y and Zhang H Q 2002 J. Phys. A 35 8253
[11]	Gao Y T and Tian B 2001 Comput. Phys. Commun. 133 158
[12]	Fan E G 2003 J. Phys. A 36 7009
[13]	Li B, Chen Y and Li Y Q 2008 Z. Naturforsch. 63a 763
[14]	Serkin V and Hasegawa A 2000 Phys. Rev. Lett. 85 4502
[15]	Ponomarenko S A and Agrawal G P 2006 Phys. Rev. Lett. 97 013901
[16]	Serkin V N, Hasegawa A and Belyaeva T L 2007 Phys. Rev. Lett. 98 074102
[17]	Wang J, Li B and Ye W C 2010 Commun. Theor. Phys. 53 698
[18]	Hasegawa A and Kodama Y 1995 Solitons in Optical Communications (Oxford: Oxford University Press)
[19]	Li L, Li Z H, Li S Q and Zhou G S 2004 Opt. Commun. 234 169
[20]	Li Z D, Li Q Y, He P B, Bai Z G and Sun Y B 2007 Ann. Phys. 322 2945
[21]	Zhang H P, Li B and Chen Y 2010 Chin. Phys. B 19 060302
[22]	Li B 2007 Int. J. Mod. Phys. C 18 1187
[23]	Li H M, Li Y S and Lin J 2009 Chin. Phys. B 18 3657
[24]	Wang H and Li B 2011 Chin. Phys. B 20 040203
[25]	Zhang H P, Li B, Chen Y and Huang F 2010 Chin. Phys. B 19 020201
[26]	Anderson M H, Ensher J R, Matthews M R, Wieman C E and Cornell E A 1995 Science 269 198
[27]	Bradley C C, Sackett C A, Tollett J J and Hulet R G 1995 Phys. Rev. Lett. 75 1687
[28]	Davis K B, Mewes M O, Andrews M R, van Druten N J, Durfee D S, Kurn D M and Ketterle W 1995 Phys. Rev. Lett. 75 3969
[29]	Dalfovo F, Giorgini F, Pitaevskii L P and Stringari S 1999 Rev. Mod. Phys. 71 463
[30]	Lü B B, Hao X and Tian Q 2011 Chin. Phys. B 20 020308
[31]	Wang Z X, Ni Z G, Cong F Z, Liu X S and Chen L 2010 Chin. Phys. B 19 113205
[32]	Wang B, Tan L, Lü C H and Tan W T 2010 Chin. Phys. B 19 117402
[33]	Li B, Zhang X F, Li Y Q, Chen Y and Liu W M 2008 Phys. Rev. A 78 023608
[34]	Qi R, Yu X L, Li Z B and Liu W M 2009 Phys. Rev. Lett. 102 185301
	Hu X H, Zhang X F, Zhao D, Luo H G and Liu W M 2009 Phys. Rev. A 79 023619
[36]	Wu L, Li L, Zhang J F, Mihalache D, Malomed B A and Liu W M 2010 Phys. Rev. A 81 061805(R)
[37]	Hu X and Li B 2011 Chin. Phys. B 20 050315
[38]	Yan Z Y and Konotop V V 2009 Phys. Rev. E 80 036607
[39]	Yan Z Y and Hang C 2009 Phys. Rev. A 80 063626
[40]	Gao Y and Lou S Y 2009 Commun. Thoer. Phys. 52 1031
[41]	Zheng L and Tang Y 2010 Chin. Phys. B 19 044209
[42]	Belic M, Nikola P, Zhong W P, Xie R H and Chen G 2008 Phys. Rev. Lett. 101 123904

Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 42

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	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.
[2]	Chang-Tong Liang(梁畅通), Jing-Jing Zhang(张晶晶), and Peng-Cheng Li(李鹏程). Phase-coherence dynamics of frequency-comb emission via high-order harmonic generation in few-cycle pulse trains[J]. 中国物理B, 2023, 32(3): 33201-033201.
[3]	Lei Chen(陈磊), Pan Li(李磐), He-Shan Liu(刘河山), Jin Yu(余锦), Chang-Jun Ke(柯常军), and Zi-Ren Luo(罗子人). Coupled-generalized nonlinear Schrödinger equations solved by adaptive step-size methods in interaction picture[J]. 中国物理B, 2023, 32(2): 24213-024213.
[4]	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.
[5]	Zhi-Xian Lei(雷志仙), Qing-Yun Xu(徐清芸), Zhi-Jie Yang(杨志杰), Yong-Lin He(何永林), and Jing Guo(郭静). Photoelectron momentum distributions of Ne and Xe dimers in counter-rotating circularly polarized laser fields[J]. 中国物理B, 2022, 31(6): 63202-063202.
[6]	Li-Jun Chang(常莉君), Yi-Fan Mo(莫一凡), Li-Ming Ling(凌黎明), and De-Lu Zeng(曾德炉). Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation[J]. 中国物理B, 2022, 31(6): 60201-060201.
[7]	Xiao-Hua Wang(王晓华), Chang-Yuan Chen(陈昌远), Yuan You(尤源), Fa-Lin Lu(陆法林), Dong-Sheng Sun(孙东升), and Shi-Hai Dong(董世海). Exact solutions of the Schrödinger equation for a class of hyperbolic potential well[J]. 中国物理B, 2022, 31(4): 40301-040301.
[8]	Shun Wang(王顺) and Wei-Chao Jiang(姜维超). Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator[J]. 中国物理B, 2022, 31(1): 13201-013201.
[9]	Shun Wang(王顺), Shahab Ullah Khan, Xiao-Qing Tian(田晓庆), Hui-Bin Sun(孙慧斌), and Wei-Chao Jiang(姜维超). Comparative study of photoionization of atomic hydrogen by solving the one- and three-dimensional time-dependent Schrödinger equations[J]. 中国物理B, 2021, 30(8): 83301-083301.
[10]	Eyube E S, Rawen B O, and Ibrahim N. Approximate analytical solutions and mean energies of stationary Schrödinger equation for general molecular potential[J]. 中国物理B, 2021, 30(7): 70301-070301.
[11]	Zillur Rahman, M Zulfikar Ali, and Harun-Or Roshid. Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method[J]. 中国物理B, 2021, 30(5): 50202-050202.
[12]	Changming Huang(黄长明), Hanying Deng(邓寒英), Liangwei Dong(董亮伟), Ce Shang(尚策), Bo Zhao(赵波), Qiangbo Suo(索强波), and Xiaofang Zhou(周小芳). Optical solitons supported by finite waveguide lattices with diffusive nonlocal nonlinearity[J]. 中国物理B, 2021, 30(12): 124204-124204.
[13]	Wen-Yan Zhang(张文艳), Kun Yang(杨坤), Li-Jie Geng(耿利杰), Nan-Nan Liu(刘楠楠), Yun-Qi Hao(郝蕴琦), Tian-Hao Xian(贤天浩), and Li Zhan(詹黎). Generation of domain-wall solitons in an anomalous dispersion fiber ring laser[J]. 中国物理B, 2021, 30(11): 114212-114212.
[14]	Yagang Zhang(张亚港), Yuheng Pei(裴宇恒), Yibo Yuan(袁一博), Feng Wen(问峰), Yuzong Gu(顾玉宗), and Zhenkun Wu(吴振坤). Propagations of Fresnel diffraction accelerating beam in Schrödinger equation with nonlocal nonlinearity[J]. 中国物理B, 2021, 30(11): 114209-114209.
[15]	Ying Yang(杨颖), Yu-Xiao Gao(高玉晓), and Hong-Wei Yang(杨红卫). Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients[J]. 中国物理B, 2021, 30(11): 110202-110202.