Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber

doi:10.1088/1674-1056/ab7442

中国物理B ›› 2020, Vol. 29 ›› Issue (3): 30202-030202.doi: 10.1088/1674-1056/ab7442

Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber

Zhong Du(杜仲), Bo Tian(田播), Qi-Xing Qu(屈启兴), Xue-Hui Zhao(赵学慧)

1 State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2 School of Information, University of International Business and Economics, Beijing 100029, China

收稿日期:2019-12-18 修回日期:2020-01-07 出版日期:2020-03-05 发布日期:2020-03-05
通讯作者: Bo Tian E-mail:tian_bupt@163.com
基金资助:
Project supported by the BUPT Excellent Ph.D. Students Foundation (Grant No. CX2019201), the National Natural Science Foundation of China (Grant Nos. 11772017 and 11805020), the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (Grant No. IPOC: 2017ZZ05), and the Fundamental Research Funds for the Central Universities of China (Grant No. 2011BUPTYB02).

Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber

Zhong Du(杜仲)¹, Bo Tian(田播)¹, Qi-Xing Qu(屈启兴)², Xue-Hui Zhao(赵学慧)¹

1 State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2 School of Information, University of International Business and Economics, Beijing 100029, China

Received:2019-12-18 Revised:2020-01-07 Online:2020-03-05 Published:2020-03-05
Contact: Bo Tian E-mail:tian_bupt@163.com
Supported by:
Project supported by the BUPT Excellent Ph.D. Students Foundation (Grant No. CX2019201), the National Natural Science Foundation of China (Grant Nos. 11772017 and 11805020), the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (Grant No. IPOC: 2017ZZ05), and the Fundamental Research Funds for the Central Universities of China (Grant No. 2011BUPTYB02).

摘要/Abstract

摘要： Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion (GVD) and fourth-order dispersion (FOD) coefficients are the constants, we exhibit the first- and second-order vector semi-rational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first- and second-order periodic vector semi-rational rogue waves, first- and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.

Abstract: Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion (GVD) and fourth-order dispersion (FOD) coefficients are the constants, we exhibit the first- and second-order vector semi-rational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first- and second-order periodic vector semi-rational rogue waves, first- and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.

中图分类号: (Integrable systems)

02.30.Ik

42.65.Tg (Optical solitons; nonlinear guided waves) 04.30.Nk (Wave propagation and interactions)

杜仲, 田播, 屈启兴, 赵学慧. Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber[J]. 中国物理B, 2020, 29(3): 30202-030202.

Zhong Du(杜仲), Bo Tian(田播), Qi-Xing Qu(屈启兴), Xue-Hui Zhao(赵学慧). Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber[J]. Chin. Phys. B, 2020, 29(3): 30202-030202.

参考文献 38

[1]	Kowal D, Urbanczyk W and Mergo P 2018 Sensors-Basel 18 915 doi: 10.3390/s18030915
[2]	Khaykovich L, Schreck F, Ferrari G, Bourdel T, Cubizolles J, Carr L D, Castin Y and Salomon C 2002 Science 296 1290 doi: 10.1126/science.1071021
[3]	Lan Z Z and Su J J 2019 Nonlinear Dyn. 96 2535 doi: 10.1007/s11071-019-04939-1
[4]	Musslimani Z H, Makris K G, El-Ganainy R and Christodoulides D N 2008 Phys. Rev. Lett. 100 030402 doi: 10.1103/PhysRevLett.100.030402
[5]	Xie X Y and Meng G Q 2019 Eur. Phys. J. Plus 134 359 doi: 10.1140/epjp/i2019-12726-7
[6]	Messouber A, Triki H, Azzouzi F, Zhou Q, Biswas A, Moshokoa S P and Belic M 2018 Opt. Commun. 425 64 doi: 10.1016/j.optcom.2018.04.051
[7]	Xie X Y, Yang S K, Ai C H and Kong L C 2020 Phys. Lett. A 384 126119 doi: 10.1016/j.physleta.2019.126119
[8]	Akhmediev N, Soto-Crespo J M and Ankiewicz A 2009 Phys. Rev. A 80 043818 doi: 10.1103/PhysRevA.80.043818
[9]	Mahnke C and Mitschke F 2012 Phys. Rev. A 85 033808 doi: 10.1103/PhysRevA.85.033808
[10]	Akhmediev N, Dudley J M, Solli D R and Turitsyn S K 2013 J. Opt. 15 060201 doi: 10.1088/2040-8978/15/6/060201
[11]	Wang L, Zhang J H, Wang Z Q, Liu C, Li M, Qi F H and Guo R 2016 Phys. Rev. E 93 012214 doi: 10.1103/PhysRevE.93.012214
[12]	Wang X B, Tian S F and Zhang T T 2018 Proc. Am. Math. Soc. 146 3353 doi: 10.1090/proc/13765
[13]	Solli D R, Ropers C, Koonath P and Jalali B 2007 Nature 450 1054 doi: 10.1038/nature06402
[14]	Wang X B, Tian S F, Feng L L and Zhang T T 2018 J. Math. Phys. 59 073505 doi: 10.1063/1.5046691
[15]	Akhmediev N, Ankiewicz A and Taki M 2009 Phys. Lett. A 373 675 doi: 10.1016/j.physleta.2008.12.036
[16]	Liu Y K and Li B 2017 Chin. Phys. Lett. 34 10202 doi: 10.1088/0256-307X/34/1/010202
[17]	Zhao L C, Yang Z Y and Yang W L 2019 Chin. Phys. B 28 010501 doi: 10.1088/1674-1056/28/1/010501
[18]	Chen S, Soto-Crespo J M, Baronio F, Grelu P and Mihalache D 2016 Opt. Exp. 24 15251 doi: 10.1364/OE.24.015251
[19]	Ankiewicz A, Kedziora D J and Akhmediev N 2011 Phys. Lett. A 375 2782 doi: 10.1016/j.physleta.2011.05.047
[20]	Lecaplain C, Grelu P, Soto-Crespo J M and Akhmediev N 2012 Phys. Rev. Lett. 108 233901 doi: 10.1103/PhysRevLett.108.233901
[21]	Wang X B and Han B 2020 J. Phys. Soc. Jpn. 89 014001 doi: 10.7566/JPSJ.89.014001
[22]	Baronio F, Degasperis A, Conforti M and Wabnitz S 2012 Phys. Rev. Lett. 109 044102 doi: 10.1103/PhysRevLett.109.044102
[23]	Degasperis A and Lombardo S 2013 Phys. Rev. E 88 052914 doi: 10.1103/PhysRevE.88.052914
[24]	Wang X B and Han B 2019 Europhys. Lett. 126 15001 doi: 10.1209/0295-5075/126/15001
[25]	Zhang G and Yan Z 2019 Proc. R. Soc. A 475 20180625 doi: 10.1098/rspa.2018.0625
[26]	Zhang G and Yan Z 2018 Proc. R. Soc. A 474 20170688 doi: 10.1098/rspa.2017.0688
[27]	Zhang G and Yan Z 2018 Commun. Nonlinear Sci. Numer. Simulat. 62 117 doi: 10.1016/j.cnsns.2018.02.008
[28]	Zhong W P, Belić M and Malomed B A 2015 Phys. Rev. E 92 053201 doi: 10.1103/PhysRevE.92.053201
[29]	Liu D Y, Tian B and Xie X Y 2017 Laser Phys. 27 035403 doi: 10.1088/1555-6611/aa4ff5
[30]	Li M Z, Tian B, Qu Q X, Chai H P, Liu L and Du Z 2017 Superlattice. Microst. 112 20 doi: 10.1016/j.spmi.2017.08.053
[31]	Du Z, Tian B, Chai H P, Sun Y and Zhao X H 2018 Chaos Soliton. Fract. 109 90 doi: 10.1016/j.chaos.2018.02.017
[32]	Gao X Y 2019 Appl. Math. Lett. 91 165 doi: 10.1016/j.aml.2018.11.020
[33]	Gao X Y, Guo Y J and Shan W R 2020 Appl. Math. Lett. 104 106170 doi: 10.1016/j.aml.2019.106170
[34]	Su J J, Gao Y T, Deng G F and Jia T T 2019 Phys. Rev. E 100 042210 doi: 10.1103/PhysRevE.100.042210
[35]	Jia T T, Gao Y T, Deng G F and Hu L 2019 Nonlinear Dyn. 98 269 doi: 10.1007/s11071-019-05188-y
[36]	Deng G F, Gao Y T, Su J J, Ding C C and Jia T T 2020 Nonlinear Dyn. 99 1039 doi: 10.1007/s11071-019-05328-4
[37]	Ablowitz M J, Kaup D J, Newell A C and Segur H 1973 Phys. Rev. Lett. 31 125 doi: 10.1103/PhysRevLett.31.125
[38]	Guo B, Ling L and Liu Q 2012 Phys. Rev. E 85 026607 doi: 10.1103/PhysRevE.85.026607

Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber

Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 38

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	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.
[2]	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.
[3]	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.
[4]	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.
[5]	Yu-Qiang Yuan(袁玉强), Xiao-Yu Wu(武晓昱), and Zhong Du(杜仲). Rogue waves of a (3+1)-dimensional BKP equation[J]. 中国物理B, 2022, 31(12): 120202-120202.
[6]	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.
[7]	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.
[8]	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.
[9]	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.
[10]	Wu-Yang Zhu(朱伍洋), Yi-Fei Pu(蒲亦非), Bo Liu(刘博), Bo Yu(余波), and Ji-Liu Zhou(周激流). A mathematical analysis: From memristor to fracmemristor[J]. 中国物理B, 2022, 31(6): 60204-060204.
[11]	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.
[12]	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.
[13]	Jian-Wen Wu(吴剑文), Yue-Jin Cai(蔡跃进), and Ji Lin(林机). Residual symmetries, consistent-Riccati-expansion integrability, and interaction solutions of a new (3+1)-dimensional generalized Kadomtsev—Petviashvili equation[J]. 中国物理B, 2022, 31(3): 30201-030201.
[14]	Hongcai Ma(马红彩), Yuxin Wang(王玉鑫), and Aiping Deng(邓爱平). Soliton molecules and asymmetric solitons of the extended Lax equation via velocity resonance[J]. 中国物理B, 2022, 31(1): 10201-010201.
[15]	Jian Wang(王健), Yi Qiao(乔艺), Junpeng Cao(曹俊鹏), and Wen-Li Yang(杨文力). Exact solution of an integrable quantum spin chain with competing interactions[J]. 中国物理B, 2021, 30(11): 117501-117501.