Four-soliton solution and soliton interactions of the generalized coupled nonlinear Schrödinger equation

doi:10.1088/1674-1056/ab84ce

中国物理B ›› 2020, Vol. 29 ›› Issue (6): 64211-064211.doi: 10.1088/1674-1056/ab84ce

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Four-soliton solution and soliton interactions of the generalized coupled nonlinear Schrödinger equation

Li-Jun Song(宋丽军), Xiao-Ya Xu(徐晓雅), Yan Wang(王艳)

Department of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China

收稿日期:2019-12-30 修回日期:2020-02-25 出版日期:2020-06-05 发布日期:2020-06-05
通讯作者: Li-Jun Song E-mail:songlij@sxu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11705108).

Four-soliton solution and soliton interactions of the generalized coupled nonlinear Schrödinger equation

Li-Jun Song(宋丽军), Xiao-Ya Xu(徐晓雅), Yan Wang(王艳)

Department of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China

Received:2019-12-30 Revised:2020-02-25 Online:2020-06-05 Published:2020-06-05
Contact: Li-Jun Song E-mail:songlij@sxu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11705108).

摘要/Abstract

摘要： Based on the generalized coupled nonlinear Schrödinger equation, we obtain the analytic four-bright-bright soliton solution by using the Hirota bilinear method. The interactions among four solitons are also studied in detail. The results show that the interaction among four solitons mainly depends on the values of solution parameters; k₁ and k₂ mainly affect the two inboard solitons while k₃ and k₄ mainly affect the two outboard solitons; the pulse velocity and width mainly depend on the imaginary part of k_i (i=1, 2, 3, 4), while the pulse amplitude mainly depends on the real part of k_i (i=1, 2, 3, 4).

Abstract: Based on the generalized coupled nonlinear Schrödinger equation, we obtain the analytic four-bright-bright soliton solution by using the Hirota bilinear method. The interactions among four solitons are also studied in detail. The results show that the interaction among four solitons mainly depends on the values of solution parameters; k₁ and k₂ mainly affect the two inboard solitons while k₃ and k₄ mainly affect the two outboard solitons; the pulse velocity and width mainly depend on the imaginary part of k_i (i=1, 2, 3, 4), while the pulse amplitude mainly depends on the real part of k_i (i=1, 2, 3, 4).

中图分类号: (Nonlinear optics)

42.65.-k

11.10.Lm (Nonlinear or nonlocal theories and models) 42.65.Tg (Optical solitons; nonlinear guided waves)

宋丽军, 徐晓雅, 王艳. Four-soliton solution and soliton interactions of the generalized coupled nonlinear Schrödinger equation[J]. 中国物理B, 2020, 29(6): 64211-064211.

Li-Jun Song(宋丽军), Xiao-Ya Xu(徐晓雅), Yan Wang(王艳). Four-soliton solution and soliton interactions of the generalized coupled nonlinear Schrödinger equation[J]. Chin. Phys. B, 2020, 29(6): 64211-064211.

参考文献 32

[1]	Wright O C, Gregory F M and Mclaughlin K T R 1999 Phys. Lett. A 257 170 doi: 10.1016/S0375-9601(99)00300-X
[2]	Sun J J and Ma S W 2015 J. Math. Phys. 56 022110 doi: 10.1063/1.4909527
[3]	Belanger N and Belanger P A 1996 Opt. Commun. 124 301 doi: 10.1016/0030-4018(95)00659-1
[4]	Mofiz U A 2007 Phys. Plasmas. 14 112906 doi: 10.1063/1.2811931
[5]	Chen Y J 1989 J. Appl. Phys. 66 43 doi: 10.1063/1.343843
[6]	Sun W R, Liu D Y and Xie X Y 2017 Chaos 27 043114 doi: 10.1063/1.4981907
[7]	Tang X Y, Guo Y and Shukla P K 2011 Eur. Phys. J. D 61 677 doi: 10.1140/epjd/e2010-09660-y
[8]	Wang Z and Cui S B 2015 J. Math. Phys. 56 021503 doi: 10.1063/1.4906937
[9]	Qi F H, Ju H M and Meng X H 2014 Nonlinear Dyn. 77 1331 doi: 10.1007/s11071-014-1382-5
[10]	Zhong X Q, Tang T T, Xiang A P and Cheng K 2011 Opt. Commun. 284 4727 doi: 10.1016/j.optcom.2011.06.013
[11]	Calegar F, Vozzi C and Gasilov S 2008 Phys. Rev. Lett. 100 123006 doi: 10.1103/PhysRevLett.100.123006
[12]	Chen D, Sun B and Wei Y 2010 Laser Phys. 20 1733 doi: 10.1134/S1054660X10150065
[13]	Song S S, Howard S S and Liu Z J 2006 Appl. Phys. Lett. 89 041115 doi: 10.1063/1.2236296
[14]	Fischer B, Cronin-Golomb M, White J and Yariv A 1981 Opt. Lett. 6 519 doi: 10.1364/OL.6.000519
[15]	Yajima T and Souma H 1978 Phys. Rev. A 17 309 doi: 10.1103/PhysRevA.17.309
[16]	Wang D S, Zhang D J and Yang J K 2010 J. Math. Phys. 51 023510 doi: 10.1063/1.3290736
[17]	Vishnu P N and Senthilvelan M 2016 Commun. Nonlinear Sci. Numer. Simulat. 36 366 doi: 10.1016/j.cnsns.2015.12.016
[18]	Lu X and Peng M S 2013 Nonlinear Dyn. 73 405 doi: 10.1007/s11071-013-0795-x
[19]	Hua S H and Mihalache D 2015 J. Phys. A: Math. Theor. 48 215202 doi: 10.1088/1751-8113/48/21/215202
[20]	Vijayajayanthi M, Kanna T and Lakshmanan M 2008 Phys. Rev. A 77 013820 doi: 10.1103/PhysRevA.77.013820
[21]	Wang Y F, Tian B, Li M, Wang P and Wang M 2014 Commun. Nonlinear Sci. Numer. Simulat. 19 1783 doi: 10.1016/j.cnsns.2013.09.003
[22]	Musammil N M, Porsezian K, Subha P A and Nithyanandan K 2017 Chaos 27 023113 doi: 10.1063/1.4976514
[23]	Zhang H Q and Ma W X 2014 Appl. Math. Comput. 230 509
[24]	Agalarov A, Zhulego V and Gadzhimuradov T 2015 Phys. Rev. E 91 042909 doi: 10.1103/PhysRevE.91.042909
[25]	Vishnu P N, Senthilvelan M and Lakshmanan M 2014 Phys. Rev. E 89 062901 doi: 10.1103/PhysRevE.89.062901
[26]	Khare A and Saxena A 2015 J. Math. Phys. 56 032104 doi: 10.1063/1.4914335
[27]	Du Z, Tian B, Chai H B, Sun Y and Zhao X H 2018 Chaos 109 90
[28]	Esen A, Sulaiman T A, Bulut H and Baskonus H M 2018 Optik 167 150 doi: 10.1016/j.ijleo.2018.04.015
[29]	Song J Y, Hao H Q and Zhang X M 2018 Appl. Math. Lett. 78 126 doi: 10.1016/j.aml.2017.11.012
[30]	Wang H and Li B 2011 Chin. Phys. B 20 040203 doi: 10.1088/1674-1056/20/4/040203
[31]	Zuo J M and Zhang Y M 2011 Chin. Phys. B 20 010205 doi: 10.1088/1674-1056/20/1/010205
[32]	Li M M, Hu C L, Wu J, Lai X J and Wang Y Y 2019 Chin. Phys. B 28 120502 doi: 10.1088/1674-1056/ab5188

Four-soliton solution and soliton interactions of the generalized coupled nonlinear Schrödinger equation

Four-soliton solution and soliton interactions of the generalized coupled nonlinear Schrödinger equation

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