Self-phase modulation via similariton solutions of the perturbed NLSE Modulation instability and induced self-steepening

Abdel‐Gawad, H. I.

doi:10.1088/1572-9494/ac6e5d

Cited by 3 publications

(1 citation statement)

References 39 publications

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“…x w) , ( (| w | 2 w) x ) and ( | w | 2 w x ) respectively (Abdel-Gawad 2022). The effects of the coefficients of group velocity dispersion, self-frequency shift and SS terms on the optical solitons of the (3+1)-dimensional nonlinear Schrödinger equation (NLSE) were investigated in Wu et al (2022).…”

Section: Introductionmentioning

confidence: 99%

Internet traffic prediction analog to solitons propagation in optical fibers via the concatenation model and stability analysis

Abdel-Gawad,

Abdel-Gawad

2024

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Internet traffic (IT) is a measure of data transfer across devices. In this paper, an analogy is made between data transfer and soliton propagation in optical fibers. This is achieved by employing the concatenation model (CM) that describes soliton propagation in optical fibers, which is presented recently in the literature. The CM contains nonlinear space-time dispersion effect, that may lead to bottleneck soliton shape (BNSS). Thus, in view of this model, BNSS effect of soliton propagation may occur, which is analogous to a possible BN in IT. So, the prediction of the characteristics of internet traffic can be depicted via the CM, which is studied here with Caputo-q time derivative. Also, a variety of exact solutions of the CM are derived. These solutions are represented graphically and they show multiple shapes of concatenated solitons. Among them, bottleneck, M-shaped, hybrid M shaped, chirped solitons and vector of dromian patterns. On the other side, the speed of IT and chips heating are estimated. It is found that the speed of IT is constant with time and the effects of distributed time delay (recent memory (RM)) is to slow the traffic speed. This is done via varying the fractional order. Also, it is observed, when accounting for RM, that the chip heating is too small. We think that the results for the speed of IT and chip heat are, qualitatively, realistic. The stability of a steady state solution is analyzed and the controlled parameters for stability is determined.

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Section: Introductionmentioning

confidence: 99%

Internet traffic prediction analog to solitons propagation in optical fibers via the concatenation model and stability analysis

Abdel-Gawad,

Abdel-Gawad

2024

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Approximate-analytic optical soliton solutions of a modified-Gerdjikov–Ivanov equation: modulation instability

Abdel‐Gawad

2023

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The Gerdjikov–Ivanov equation (GIE) occupied a remarkable area of research in the literature. In the present work, a modified GIE (MGIE) is considered which is new and was not studied in the literature. Also, the modified-unified method (MUM) is used to obtain approximate analytic solutions (AASs) of MGIE. Up to our knowledge, no AASs for non-integrable complex field equation were found up to now. Thus the AASs found, here, are novel. The UM addresses finding the exact solutions to integrable equations. In this sense as no exact solution for MGIE exists, consequently, it is not integrable. So, here, approximate analytic optical soliton solutions are invoked. The UM stands for expressing the solution of nonlinear evolution equations in polynomial and rational forms in an auxiliary function (AF) with an appropriate auxiliary equation. For finding exact solutions by the UM, the coefficients of the AF, with all powers, are set equal to zero, For a non-integrable equation, only approximate solutions are affordable. In this case, we are led to utilizing the MUM. Herein, non-zero coefficients (residue terms (RTs)) are considered as errors, which are space and time-independent. It is worth mentioning that, this is in contrast to the errors found by the different numerical methods, where they are space and time-dependent. Further, in the present case, the maximum error is controlled via an adequate choice of the parameters in the RTs. These solutions are displayed in graphs. Breather soliton, chirped soliton and M-shape soliton, among others, are observed. Furthermore, modulation instability (MI) is studied and it is found MI triggers when the coefficient of the nonlinear dispersion exceeds a critical value.

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RETRACTED: On extracting novel optical solutions to a higher order nonlinear Schrödinger’s equation

Nonlaopon¹,

Alharthi²,

Alqurashi³

et al. 2022

Results in Physics

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Self-phase modulation via similariton solutions of the perturbed NLSE Modulation instability and induced self-steepening

Cited by 3 publications

References 39 publications

Internet traffic prediction analog to solitons propagation in optical fibers via the concatenation model and stability analysis

Internet traffic prediction analog to solitons propagation in optical fibers via the concatenation model and stability analysis

Approximate-analytic optical soliton solutions of a modified-Gerdjikov–Ivanov equation: modulation instability

RETRACTED: On extracting novel optical solutions to a higher order nonlinear Schrödinger’s equation

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