Optical solitons with Radhakrishnan–Kundu–Lakshmanan equation by Laplace–Adomian decomposition method

González-Gaxiola, O.; Biswas, Anjan

doi:10.1016/j.ijleo.2018.10.173

Cited by 56 publications

(13 citation statements)

References 9 publications

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“…Substituting (17) and (18) into Eq. (16) gives rise to Hence, Eq. 20suggests the following iterative algorithm…”

Section: The Laplace Adomian Decomposition Methods (Ladm)mentioning

confidence: 99%

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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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“…Substituting (17) and (18) into Eq. (16) gives rise to Hence, Eq. 20suggests the following iterative algorithm…”

Section: The Laplace Adomian Decomposition Methods (Ladm)mentioning

confidence: 99%

“…One of the very many and modern numerical algorithms that will be implemented is the Laplace-Adomian decomposition integration scheme. This method has been successfully applied to variety of other models from optics [14][15][16]. This paper now studies FLE, for the first time, by the aid of Laplace-Adomian decomposition scheme.…”

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 study aims to examine numerous exact solutions including bright-dark soliton solutions, Jacobi elliptic solutions of the conformable time-fractional perturbed Radhakrishnan-Kundu-Lakshmanan (RKL) equation [17][18][19] via GJEF method for the first time in the conformable time fractional RKL model. The dynamics of the light pulses were studied and represented by various NLPDEs including RKL equation.…”

Section: Introductionmentioning

confidence: 99%

“…The coefficient a represents the group-velocity dispersion (GVD), b represents the coefficient of nonlinearity, Ω symbolises the inter-modal dispersion (IMD) and Λ, σ, Υ signify the coefficient of selfsteepening for short pulses, the higher-order dispersion coefficient and the third order dispersion term respectively. As soon as we substitue α = 1 in the time fractional perturbed RKL equation, we obtain the original Radhakrishnan-Kundu-Lakshmanan equation [18]. This paper is structured as follows: In sec.…”

Section: Introductionmentioning

confidence: 99%

Optical soliton solutions of the conformable time fractional Radhakrishnan–Kundu–Lakshmanan Model

Yadav

Gupta

2022

Opt Quant Electron

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In the present study, we have obtained different kinds of wave solutions which possess distinctive physical characteristics of the nonlinear conformable time fractional Radhakrishnan-Kundu-Lakshmanan model by utilizing the generalized Jacobi elliptic function (GJEF) method. 3-D surfaces to some of the reported solutions are plotted and the dependence of the behaviour of the solutions on the fractional derivative has also been analyzed in the present study. In addition to providing physical explanations of Radhakrishnan-Kundu-Lakshmanan equation, the solutions presented here may also provide an insight into the the study of wave propagation in various conformable fractional nonlinear models arising in nonlinear sciences.

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“…An advantage of this method is that it can provide analytical approximation or an approximated solution to a wide class of nonlinear equations without linearization, perturbation, closure approximation or discretization methods [33]. A recent work has been done by Biswas et al [34] on optical solitons by using the Laplace-Adomian decomposition method. As a result numerical dispersive bright and dark optical solitons have been displayed and the precision obtained is excellent.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions to Generalized Nonlinear Schrödinger Equation by Adomian Decomposition Technique

Adanhounme

Edah

Hounkonnou

2019

AIR

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We study the higher-order nonlinear Schrödinger equation which takes care of the second as well as third order dispersion effects, cubic and quintic self phase modulations, self steepening and nonlinear dispersion effects. Taking advantage of the initial condition, we transform theprevious equation into a nonlinear functional equation to which we apply a powerful analytical method called the Adomian decomposition method. We compute the Adomian’s polynomials of corresponding infinite series solution. Assuming that the initial condition and all its derivatives converge to zero sufficiently rapidly as the time approaches to infinity, we established the convergence of the previous series. The last part of the paper describes applications resulting from nonlinear propagation phenomena in optical fibers. Numerical simulations are developed and it is further shown that comparison with other results yields a good qualitative agreement. These results demonstrate the robustness of the proposed method.

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Optical solitons with Radhakrishnan–Kundu–Lakshmanan equation by Laplace–Adomian decomposition method

Cited by 56 publications

References 9 publications

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

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

Optical soliton solutions of the conformable time fractional Radhakrishnan–Kundu–Lakshmanan Model

Analytical Solutions to Generalized Nonlinear Schrödinger Equation by Adomian Decomposition Technique

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