Journal of Quantum Optics, Volume. 28, Issue 1, 18(2022)

Influence of Higher-order Effects on N-soliton Solution of the Coupled Nonlinear Schrdinger Equation

SONG Li-jun* and FANG Wen-jing
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    References(36)

    [1] [1] TIAN Q, WU L, ZHANG J F, et al. Exact soliton solutions and their stability control in the nonlinear Schrdinger equation with spatiotemporally modulated nonlinearity[J]. Physical Review E, 2011, 83(1): 16602. DOI: 10.1103/physreve.83.016602.

    [2] [2] ZHANG H F, HAO H Q, ZHANG J W. Breathers and Soliton Solutions for a Generalization of the Nonlinear Schrdinger Equation[J]. Mathematical Problems in Engineering, 2013, 2: 456864. DOI: 10.1155/2013/456864.

    [3] [3] WU G, DAI C. Nonautonomous soliton solutions of variable-coefficient fractional nonlinear Schrdinger equation[J]. Applied Mathematics Letters, 2020, 106: 106365. DOI: 10.1016/j.aml.2020.106365

    [4] [4] WANG M, TIAN B. In an inhomogeneous multicomponent optical fiber: Lax pair, generalized Darboux transformation and vector breathers for a three-coupled variable-coefficient nonlinear Schrdinger system[J]. European Physical Journal Plus, 2021, 136(10): 1002. DOI: 10.1140/epjp/s13360-021-01918-7.

    [5] [5] KODAMA Y, HASEGAWA A. Nonlinear pulse propagation in a monomode dielectric guide[J]. IEEE J. Quantum Electron, 1987, 23: 510-524. DOI: 10.1109/JQE.1987.1073392.

    [6] [6] MIRZAZADEH M, ARNOUS A H, MAHMOOD M F, et al. Soliton solutions to resonant nonlinear Schrdinger’s equation with time-dependent coefficients by trial solution approach[J]. Nonlinear dynamics, 2015, 81(1-2): 277-282. DOI: 10.1007/s11071-015-1989-1.

    [7] [7] BONGIOVANNI D, LI Z L, WETZEL B, et al. Third-order Riemann pulses in optical fibers[J]. Optics Express, 2020, 28(26): 39827-39840. DOI: 10.1364/OE.411736.

    [8] [8] SIMBAWA E, SEADAWY A R, SUGATI T G. Dispersive wave propagation of the nonlinear Sasa-Satsuma dynamical system with computational and analytical soliton solutions[J]. Chaos Solitons & Fractals, 2021, 152: 111376. DOI: 10.1016/j.chaos.2021.111376.

    [9] [9] WANG Y Y, DAI C Q, WANG X G. Stable localized spatial solitons in PT-symmetric potentials with power-law nonlinearity[J]. Nonlinear dynamics, 2014, 77(4): 1323-1330. DOI: 10.1007/s11071-014-1381-6.

    [10] [10] GENG X G, LV Y Y. Darboux transformation for an integrable generalization of the nonlinear Schrdinger equation[J]. Nonlinear dynamics, 2012, 69(4): 1621-1630. DOI: 10.1007/s11071-012-0373-7.

    [11] [11] ZHANG C C, LI C Z, HE J S. Darboux transformation and Rogue waves of the Kundu-nonlinear Schrdinger equation[J]. Mathematical Methods in the Applied Sciences, 2015, 38(11): 2411-2425. DOI: 10.1002/mma.3232.

    [12] [12] CHEN S H, SONG L Y. Peregrine solitons and algebraic soliton pairs in Kerr media considering space-time correction[J]. Physics Letters A, 2014, 378(18-19): 1228-1232. DOI: 10.1016/j.physleta.2014.02.042.

    [13] [13] WANG L, ZHU Y J, QI F H, LI M, GUO R. Modulational instability, higher-order localized wave structures, and nonlinear wave interactions for a nonautonomous Lenells-Fokas equation in inhomogeneous fibers[J]. Chaos: An Interdisciplinary Journal of Nonlinear, 2015, 25: 063111. DOI: 10.1063/1.4922025.

    [14] [14] LU X, LIN F, QI F. Analytical study on a two-dimensional Korteweg-de Vries model with bilinear representation, Backlund transformation and soliton solutions[J]. Applied Mathematical Modelling, 2015, 39: 3221-3226. DOI: 0.1016/j.apm.2014.10.046.

    [15] [15] OKAMAWARI T, HASEGAWA A, KODAMA Y, Analyses of soliton interactions by means of a perturbed inverse-scattering transform[J]. Physical Review A, 1995, 51(4): 3203-3220. DOI: 10.1103/PhysRevA.51.3203.

    [16] [16] KANNA T, LAKSHMANAN M. Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrdinger equations[J]. Physical Review Letter, 2001, 86(22): 5043-5046. DOI: 10.1103/PhysRevLett.86.5043.

    [17] [17] VIJAYAJAYANTHI M, KANNA T, LAKSHMANAN M. Bright-dark solitons and their collisions in mixed N-coupled nonlinear Schrdinger equations[J]. Physical Review A, 2008, 77(1): 013820. DOI: 10.1103/PhysRevA.77.013820.

    [18] [18] WANG M, SHAN W R, LV X. Soliton collision in a general coupled nonlinear Schrdinger system via symbolic computation[J]. Applied Mathematics and Computation, 2013, 219(24): 11258-11264. DOI: 10.1016/j.amc.2013.04.013.

    [19] [19] WANG X M, ZHANG L L. The superposition solitons for 3-coupled nonlinear Schrdinger equations[J]. Communications in Nonlinear Science and Numerical Simulation, 2017, 42: 93-105. DOI: 10.1016/j.cnsns.2016.05.011.

    [20] [20] GAO Z, SONG S, DUAN J. The application of (2+1)-dimensional coupled nonlinear Schrdinger equations with variable coefficients in optical fibers[J]. Optik- International Journal for Light and Electron Optics, 2018, 172: 953-967. DOI: 10.1016/j.ijleo.2018.06.048.

    [21] [21] DAI C Q, WANG Y Y, ZHANG J F. Controllable Akhmediev breather and Kuznetsov-Ma soliton trains in PT-symmetric coupled waveguides[J]. Optics Express, 2014, 22(24): 29862. DOI: 10.1364/OE.22.029862.

    [22] [22] XU G Q. Painleve classification of a generalized coupled Hirota system[J]. Physical Review E, 2006, 74: 027602. DOI: 10.1103/PhysRevE.74.027602.

    [23] [23] TIAN S F, ZHANG T T, ZHANG H Q. Darboux transformation and new periodic wave solutions of generalized derivative nonlinear Schrdinger equation[J]. Physica Scripta, 2009, 80(6): 065013. DOI: 10.1088/0031-8949/80/06/065013.

    [24] [24] HE J S, GUO L J, ZHANG Y S, CHABCHOUB A. Theoretical and experimental evidence of non-symmetric doubly localized rogue waves[J]. Proceedings Mathematical Physical & Engineering Sciences, 2014, 470(2171): 318. DOI: 10.1098/rspa.2014.0318.

    [25] [25] BHRAWY A H, ABDELKAWY M A, BISWAS A. Cnoidal and snoidal wave solutions to coupled nonlinear wave equations by the extended Jacobi’s elliptic function method[J]. Communications in Nonlinear Science & Numerical Simulation, 2013, 18(4): 915-925. DOI: 10.1016/j.cnsns.2012.08.034.

    [26] [26] ZHANG Y S, GUO L J, HE J S, ZHOU Z X. Darboux transformation of the second-type derivative nonlinear Schrdinger equation[J]. Letters in Mathematical Physics, 2015, 105(6): 853-891. DOI: 10.1007/s11005-015-0758-x.

    [27] [27] BISWAS A, KONAR S. Quasi-particle theory of optical soliton interaction[J]. Communications in Nonlinear Science & Numerical Simulation, 2007, 12(7): 1202-1228. DOI: 10.1016/j.cnsns.2005.11.010.

    [28] [28] KOHL R, BISWAS A, MILOVIC D, ZERRAD E. Optical soliton perturbation in a non-Kerr law media[J]. Optics & Laser Technology, 2008, 40(4): 647-662. DOI: 10.1016/j.optlastec.2007.10.002.

    [29] [29] HAMMACK J L, HENDERSON D M, SEGUR H. Progressive waves with persistent two-dimensional surface patterns in deep water[J]. Journal of Fluid Mechanics, 2005, 532(10): 1-52. DOI: 10.1017/S0022112005003733.

    [30] [30] DALFOVO F, GIORGINI S, PITAEVSKII L P, STRINGARY S. Theory of Bose-Einstein condensation in trapped gases[J]. Reviews of Modern Physics, 1999, 71(3): 463-512. DOI: 10.1103/RevModPhys.71.463.

    [31] [31] IEDA J, MIYAKAWA T, Wadati M. Matter-Wave Solitons in an F=1 Spinor Bose-Einstein Condensate[J]. Journal of the Physical Society of Japan, 2004, 73(11): 2996-3007. DOI: 10.1143/JPSJ.73.2996.

    [32] [32] TASGAL R S, POTASEK M J. Soliton solutions to coupled higher-order nonlinear Schrdinger equations[J]. Journal of Mathematical Physics, 1992, 33(3): 1208-1215. DOI: 10.1063/1.529732.

    [33] [33] WANG D S, YIN S J, TIAN Y, LIU Y F. Integrability and bright soliton solutions to the coupled nonlinear Schrdinger equation with higher-order effects[J]. Applied Mathematics and Computation, 2014, 229: 296-309. DOI: 10.1016/j.amc.2013.12.057.

    [34] [34] BINDU S G, MAHALINGAM A, PORSEZIAN K. Dark soliton solutions of the coupled Hirota equation in nonlinear fiber[J]. Physics Letters A, 2001, 286(5): 321-331. DOI: 10.1016/S0375-9601(01)00371-1.

    [35] [35] PARK Q H, SHIN H J. Higher order nonlinear optical effects on polarized dark solitons[J]. Optics Communications, 2000, 178(1-3): 233-244. DOI: 10.1016/S0030-4018(00)00648-9.

    [36] [36] PRIYA N V, SENTHILVELAN M. N-Bright-Bright and N-Dark-Dark solitons of the Coupled Generalized Nonlinear Schrdinger Equations[J]. Communications in Nonlinear Science and Numerical Simulation, 2016, 36: 366-377. DOI: 10.1016/j.cnsns.2015.12.016.

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    SONG Li-jun, FANG Wen-jing. Influence of Higher-order Effects on N-soliton Solution of the Coupled Nonlinear Schrdinger Equation[J]. Journal of Quantum Optics, 2022, 28(1): 18

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    Paper Information

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    Received: Jul. 5, 2021

    Accepted: --

    Published Online: Apr. 21, 2022

    The Author Email: SONG Li-jun (songlij@sxu.edu.cn)

    DOI:10.3788/jqo20222801.0601

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