Breather-to-soliton transition for a sixth-order nonlinear Schrödinger equation in an optical fiber

Huang, Qianglian; Gao, Yi–Tian; Hu, Lei

doi:10.1016/j.aml.2017.06.015

Cited by 51 publications

(12 citation statements)

References 20 publications

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“….) are real constant parameters, x denotes the propagation variable and, t denotes the transverse variable (time in a moving frame) [11][12][13]. In this study, we will investigate the Equation (4) which we have obtained by taking α m = 0, m = 4, 5, .…”

Section: Mathematical Modelmentioning

confidence: 99%

“…It has been observed in both experimental and numerical simulations that higher order nonlinear terms and effects should be taken into consideration in order to make the transmission in Equation 3faster (sub-picosecond or femtosecond). In this study, we will consider the third order equations iq x + α 2 (q tt + 2q |q| 2 ) − iα 3 (q ttt + 6q t |q| 2 ) = 0 (4) from the hierarchy of the higher order NLSE given in [8,[11][12][13]. Our main goal is to obtain exact analytical solutions of this equation.…”

Section: Introductionmentioning

confidence: 99%

“…This method has a finite series expansion form based on the balancing principle. Higher order NLSEs were taken into consideration by researchers in recent years [11,[29][30][31][32]. However, to the best of our knowledge, the exact solutions that contain generalized hyperbolic and trigonometric functions of third-order NLS equations have not been studied.…”

Section: Introductionmentioning

confidence: 99%

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A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws

Yaşar

Seadawy

2020

Journal of Taibah University for Science

118

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In this study, we consider the third order nonlinear Schrödinger equation (TONSE) that models the wave pulse transmission in a time period less than one-trillionth of a second. With the help of the extended modified method, we obtain numerous exact travelling wave solutions containing sets of generalized hyperbolic, trigonometric and rational solutions that are more general than classical ones. Secondly, we construct the transformation groups which left the equations invariant and vector fields with the Lie symmetry groups approach. With the help of these vector fields, we obtain the symmetry reductions and exact solutions of the equation. The obtained groupinvariant solutions are Jacobi elliptic function and exponential type. We discuss the dynamic behaviour and structure of the exact solutions for distinct solutions of arbitrary constants. Lastly, we obtain conservation laws of the considered equation by construing the complex equation as a system of two real partial differential equations (PDEs).

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Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws

Yaşar

Seadawy

2020

Journal of Taibah University for Science

118

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“…Furthermore, Darboux transformation is utilized to find out several kinds of solitons, which can be converted from breathers in the presence of real and imaginary parts of the eigenvalues. Interconnection of solitons and breathers are analyzed in the form of graph . Coupled variable‐coefficient fourth‐order NLSE is analyzed to demonstrate the simultaneous transmission of optical waves in an inhomogeneous optical fiber.…”

Section: Introductionmentioning

confidence: 98%

Generation and transmission of fractional‐order optical bright solitons in single mode fiber

Mehboob

Usman

Hussain

2019

Micro & Optical Tech Letters

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This article addresses the generation and transmission of fractional-order optical bright solitons (OBSs) in silica based single mode fiber. We take into account secondorder dispersion effect in the presence of anomalous dispersion and self-phase modulation together with third-order dispersion. Fractional-order OBS have been extracted using nonlinear Schrodinger equation. We consider dispersion dominant case with variation of data rates from 10 to 60 Gbps covering ultralong distance of 9040 km. The transmission link is composed of optical amplifier with gain of 20 dB and a noise figure of 4 dB. The analytical computations are carried out to calculate the nonlinear dispersive effects and a comparison is made between the analytical and simulated results. Erbiumdoped fiber amplifier and dispersion compensated fiber have been used to overcome fluctuations and to maintain the fractional-order OBS pulse profile. In the end, the outcomes are probed and compared on the basis of Q-factor and bit error rate (BER). It is observed that best OBS transmission result is achieved at 40 Gbps, where Q-factor is 9.85 with a corresponding BER of 2.91e −23 . K E Y W O R D S nonlinear Schrodinger equation, optical bright solitons, second-order dispersion, self-phase modulation, third-order dispersion

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“…There are also some interests on higher members of the system (1) for N ≥ 3 [28]- [40]. These methods, in particular the Hirota method, become more difficult or not available for systems N ≥ 3.…”

Section: Introductionmentioning

confidence: 99%

Special Smarandache curves in R31

GÜRSES¹,

BEKTAS²,

Yuce³

et al. 2016

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Breather-to-soliton transition for a sixth-order nonlinear Schrödinger equation in an optical fiber

Cited by 51 publications

References 20 publications

A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws

A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws

Generation and transmission of fractional‐order optical bright solitons in single mode fiber

Special Smarandache curves in R31

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