Optical soliton perturbation with Fokas–Lenells equation by mapping methods

Krishnan, E. V.; Biswas, Anjan; Zhou, Qin; Alfiras, Mohanad

doi:10.1016/j.ijleo.2018.10.017

Cited by 61 publications

(27 citation statements)

References 27 publications

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“…The modulus of chirped bright soliton solution (28) is depicted in Fig. 5(a) Herein our target is to compare the results obtained here with corresponding results of some previous studies in the literature (e.g., [22][23][24][25][26][27][28][29][30][31]). The authors in [22,23], for instance, utilized the trial equation method and the complex envelope function ansatz to examine the combined solitary wave and chirped soliton solutions of the FL equation 1when perturbation terms are neglected (i.e., α = λ = μ = 0).…”

Section: Graphical Interpretationmentioning

confidence: 79%

“…Also we mention the three methods of the modified Kudryashov's method, the exp(-ψ(η))-expansion method, and the sine-Gordon expansion method [26]. Finally, we have the semi-inverse variational principle [27], the Riccati equation method [28], the generalized exponential function method [29], the mapping method [30], the modified extended direct algebraic method [31], and the Laplace-Adomian decomposition method [32].…”

Section: Introductionmentioning

confidence: 99%

“…(1) represent inter-modal dispersion, self-steepening effect, and nonlinear dispersion, respectively. The authors in [23] investigated the chirped soliton solutions of the FL equation (1) in the absence of perturbation terms (i.e., α = λ = μ = 0) whereas the studies in [24][25][26][27][28][29][30][31][32] were devoted to the chirp-free soliton solutions of Eq. (1).…”

Section: Introductionmentioning

confidence: 99%

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Chirped optical soliton perturbation of Fokas–Lenells equation with full nonlinearity

Al-Ghafri¹,

Krishnan

Biswas

2020

Adv Differ Equ

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The present paper focuses on the chirped soliton solutions of the Fokas-Lenells equation in the presence of perturbation terms. A complex envelope traveling-wave solution is used to reduce the governing equation to an ordinary differential equation (ODE). An auxiliary equation in the form of a first-order nonlinear ODE with six-degree terms is implemented as a solution method. Various types of chirped soliton solutions including bright, dark, kink and singular solitons are extracted. The associated chirp is also determined for each of these optical pulses. Restrictions for the validity of chirped soliton solutions are presented.

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Section: Graphical Interpretationmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Chirped optical soliton perturbation of Fokas–Lenells equation with full nonlinearity

Al-Ghafri¹,

Krishnan

Biswas

2020

Adv Differ Equ

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“…Thus, a variety of powerful mathematical approaches have been developed to derive soliton solutions for many physical models. For more details, readers are referred to references [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers

Al-Ghafri

2020

Symmetry

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In this work, we investigate the conformable space–time fractional complex Ginzburg–Landau (GL) equation dominated by three types of nonlinear effects. These types of nonlinearity include Kerr law, power law, and dual-power law. The symmetry case in the GL equation due to the three types of nonlinearity is presented. The governing model is dealt with by a straightforward mathematical technique, where the fractional differential equation is reduced to a first-order nonlinear ordinary differential equation with solution expressed in the form of the Weierstrass elliptic function. The relation between the Weierstrass elliptic function and hyperbolic functions enables us to derive two types of optical soliton solutions, namely, bright and singular solitons. Restrictions for the validity of the optical soliton solutions are given. To shed light on the behaviour of solitons, the graphical illustrations of obtained solutions are represented for different values of various parameters. The symmetrical structure of some extracted solitons is deduced when the fractional derivative parameters for space and time are symmetric.

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“…One of the governing models to study dispersive solitons is Fokas-Lennels equation (FLE) [1][2][3][4][5][6][7][8][9][10][11][12][13]. In such a model, in addition to group velocity dispersion (GVD), one considers, inter-modal dispersion as well as nonlinear dispersion thus treating it with a flavor of additional dispersive effects.…”

Section: Introductionmentioning

confidence: 99%

Optical soliton perturbation of Fokas-Lenells equation by the Laplace-Adomian decomposition algorithm

González-Gaxiola¹,

Biswas²,

Belić³

2019

J. Eur. Opt. Soc.-Rapid Publ.

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This paper displays numerical simulation for bright and dark optical solitons that emerge from Fokas-Lenells equation which is studied in the context of dispersive solitons in polarization-preserving fibers. The Laplace-Adomian decomposition scheme is the numerical tool adopted in the paper. The numerical results, for bright and dark solitons, are expository and therefore supplement the analytical developments, thus far.

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Optical soliton perturbation with Fokas–Lenells equation by mapping methods

Cited by 61 publications

References 27 publications

Chirped optical soliton perturbation of Fokas–Lenells equation with full nonlinearity

Chirped optical soliton perturbation of Fokas–Lenells equation with full nonlinearity

Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers

Optical soliton perturbation of Fokas-Lenells equation by the Laplace-Adomian decomposition algorithm

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