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Optical and Quantum Electronics

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01-04-2023

Generalized periodic and soliton optical ultrashort pulses for perturbed Fokas–Lenells equation

Authors: Mahmoud Gaballah, Rehab M. El-Shiekh, Heba Hamdy

Published in: Optical and Quantum Electronics | Issue 4/2023

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Abstract

In this paper, the perturbed Fokas–Lenells equation, which describes the propagation of ultrashort optical pulses in birefringent fibers, is investigated by the generalized Jacobi elliptic expansion (GJEE) method. As a result, different types of optical solitons like periodic, kink, and bright solitons are obtained. The extracted solutions cover all the other solutions achieved in the literature. In addition, other novel general solutions were obtained which make the GJEE is most effective and powerful in comparison to other existing similar methods. The 3D, density plot, and 2D plots respectively are given for periodic, kink, and bright solitons to illustrate the different shapes of the obtained optical ultrashort pulses. The attend results have many important applications in nonlinear optics, femtochemistry, medical imaging, Micro-machining, T-rays, and frequency comb.

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Arshed, S., Biswas, A., Zhou, Q., Khan, S., Adesanya, S., Moshokoa, S.P., Belic, M.: Optical solitons pertutabation with Fokas-Lenells equation by exp(-\(\phi (\xi ))\)-expansion method. Optik (Stuttg). 179, 341–345 (2019). https://doi.org/10.1016/j.ijleo.2018.10.13ADSCrossRef

Bansal, A., Kara, A.H., Biswas, A., Moshokoa, S.P., Belic, M.: Optical soliton perturbation, group invariants and conservation laws of perturbed Fokas-Lenells equation. Chaos, Solitons Fractals. 114, 275–280 (2018). https://doi.org/10.1016/J.CHAOS.2018.06.030ADSMathSciNetCrossRefMATH

Darvishi, M.T., Khani, F.: Numerical and explicit solutions of the fifth-order Korteweg-de Vries equations. Chaos, Solitons Fractals. 39, 2484–2490 (2009). https://doi.org/10.1016/J.CHAOS.2007.07.034ADSCrossRefMATH

Darvishi, M.T., Najafi, M., Arbabi, S., Kavitha, L.: Exact propagating multi-anti-kink soliton solutions of a (3+1)-dimensional B-type Kadomtsev-Petviashvili equation. Nonlinear Dyn. 83, 1453–1462 (2016). https://doi.org/10.1007/S11071-015-2417-2/FIGURES/9MathSciNetCrossRefMATH

Darvishi, M.T., Arbabi, S., Najafi, M., Wazwaz, A.M.: Traveling wave solutions of a (2 + 1)-dimensional Zakharov-like equation by the first integral method and the tanh method. Optik (Stuttg). 127, 6312–6321 (2016). https://doi.org/10.1016/J.IJLEO.2016.04.033ADSCrossRef

Darvishi, M.T., Kavitha, L., Najafi, M., Kumar, V.S.: Elastic collision of mobile solitons of a (3 + 1)-dimensional soliton equation. Nonlinear Dyn. 86, 765–778 (2016). https://doi.org/10.1007/S11071-016-2920-0/FIGURES/13CrossRef

Dieu-donne, G., Tiofack, C.G.L., Seadawy, A., Hubert, M.B., Betchewe, G., Serge, D.Y.: Propagation of W-shaped, M-shaped and other exotic optical solitons in the perturbed Fokas-Lenells equation. Eur. Phys. J. Plus 1354(135), 1–18 (2020). https://doi.org/10.1140/EPJP/S13360-020-00382-ZCrossRef

El-Shiekh, R.M.: Jacobi elliptic wave solutions for two variable coefficients cylindrical Korteweg-de Vries models arising in dusty plasmas by using direct reduction method. Comput. Math. with Appl. (2018a). https://doi.org/10.1016/j.camwa.2017.11.031MathSciNetCrossRefMATH

El-Shiekh, R.M.: New similarity solutions for the generalized variable-coefficients KdV equation by using symmetry group method. Arab J. Basic Appl. Sci. (2018b). https://doi.org/10.1080/25765299.2018.1449343CrossRef

El-Shiekh, R.M.: Classes of new exact solutions for nonlinear Schrö dinger equations with variable coefficients arising in optical fiber. Results Phys. (2019). https://doi.org/10.1016/j.rinp.2019.102214CrossRef

El-Shiekh, R.M.: Novel solitary and shock wave solutions for the generalized variable-coefficients (2+1)-dimensional KP-Burger equation arising in dusty plasma. Chinese J. Phys. 71, 341–350 (2021). https://doi.org/10.1016/J.CJPH.2021.03.006ADSMathSciNetCrossRef

El-Shiekh, R.M., Al-Nowehy, A.-G.: Integral methods to solve the variable coefficient nonlinear Schrödinger equation. Zeitschrift fur Naturforsch. Sect. C J. Biosci. (2013). https://doi.org/10.5560/ZNA.2012-0108CrossRef

El-Shiekh, R.M., Al-Nowehy, A.G.A.A.H.: Symmetries, reductions and different types of travelling wave solutions for symmetric coupled burgers equations. Int. J. Appl. Comput. Math. 84(8), 1–13 (2022). https://doi.org/10.1007/S40819-022-01385-3MathSciNetCrossRefMATH

El-Shiekh, R.M., Gaballah, M.: Novel solitons and periodic wave solutions for Davey-Stewartson system with variable coefficients. J. Taibah Univ. Sci. 14, 783–789 (2020). https://doi.org/10.1080/16583655.2020.1774975CrossRef

El-Shiekh, R.M., Gaballah, M.: Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation. Int. J. Nonlinear Sci. Numer. Simul. (2020). https://doi.org/10.1515/ijnsns-2019-0054CrossRefMATH

El-Shiekh, R.M., Gaballah, M.: Solitary wave solutions for the variable-coefficient coupled nonlinear Schrödinger equations and Davey-Stewartson system using modified sine-Gordon equation method. J. Ocean Eng. Sci. (2020). https://doi.org/10.1016/j.joes.2019.10.003CrossRefMATH

El-Shiekh, R.M., Gaballah, M.: New rogon waves for the nonautonomous variable coefficients Schrödinger equation. Opt. Quantum Electron. 53, 1–12 (2021). https://doi.org/10.1007/S11082-021-03066-9/FIGURES/3CrossRef

El-Shiekh, R.M., Gaballah, M.: New analytical solitary and periodic wave solutions for generalized variable-coefficients modified KdV equation with external-force term presenting atmospheric blocking in oceans. J. Ocean Eng. Sci. (2021). https://doi.org/10.1016/J.JOES.2021.09.003CrossRef

El-Shiekh, R.M., Gaballah, M.: Integrability, similarity reductions and solutions for a (3+1)-dimensional modified Kadomtsev-Petviashvili system with variable coefficients. Partial Differ. Equ. Appl. Math. 6, 1–9 (2022). https://doi.org/10.1016/J.PADIFF.2022.100408CrossRef

El-Shiekh, R.M., Gaballah, M.: Lie group analysis and novel solutions for the generalized variable-coefficients Sawada-Kotera equation. Europhys. Lett. (2023). https://doi.org/10.1209/0295-5075/ACB460CrossRef

El-Shiekh, R.M., Hamdy, H.: Novel distinct types of optical solitons for the coupled Fokas-Lenells equations. Opt. Quantum Electron. 55, 1–11 (2023). https://doi.org/10.1007/S11082-023-04546-W/METRICSCrossRef

El-Shiekh, R.M., Gaballah, M., Elelamy, A.F.: Similarity reductions and wave solutions for the 3D-Kudryashov-Sinelshchikov equation with variable-coefficients in gas bubbles for a liquid. Results Phys. 40, 1–6 (2022). https://doi.org/10.1016/J.RINP.2022.105782CrossRef

Esen, H., Ozisik, M., Secer, A., Bayram, M.: Optical soliton perturbation with Fokas-Lenells equation via enhanced modified extended tanh-expansion approach. Optik (Stuttg). 267, 1–10 (2022). https://doi.org/10.1016/J.IJLEO.2022.169615CrossRef

Gaballah, M., El-Shiekh, R.M., Akinyemi, L., Rezazadeh, H.: Novel periodic and optical soliton solutions for Davey-Stewartson system by generalized Jacobi elliptic expansion method. Int. J. Nonlinear Sci. Numer. Simul. (2022). https://doi.org/10.1515/ijnsns-2021-0349CrossRef

Jhangeer, A., Rezazadeh, H., Seadawy, A.: A study of travelling, periodic, quasiperiodic and chaotic structures of perturbed Fokas-Lenells model. Pramana J. Phys. 95, 1–11 (2021). https://doi.org/10.1007/S12043-020-02067-9/FIGURES/12ADSCrossRef

Khani, F., Darvishi, M.T., Farmany, A., Kavitha, L.: New exact solutions of coupled (2+1)-dimensional nonlinear systems of Schrödinger equations. ANZIAM J. 52, 110–121 (2010). https://doi.org/10.1017/S1446181111000563MathSciNetCrossRefMATH

Krishnan, E.V., Biswas, A., Zhou, Q., Alfiras, M.: Optical soliton perturbation with Fokas-Lenells equation by mapping methods. Optik (Stuttg). 178, 104–110 (2019). https://doi.org/10.1016/j.ijleo.2018.10.017ADSCrossRef

Muniyappan, A., Sahasraari, L.N., Anitha, S., Ilakiya, S., Biswas, A., Yıldırım, Y., Triki, H., Alshehri, H.M., Belic, M.R.: Family of optical solitons for perturbed Fokas-Lenells equation. Optik (Stuttg). 249, 168224 (2022). https://doi.org/10.1016/J.IJLEO.2021.168224ADSCrossRef

Rafiq, M.N., Majeed, A., Yao, S.W., Kamran, M., Rafiq, M.H., Inc, M.: Analytical solutions of nonlinear time fractional evaluation equations via unified method with different derivatives and their comparison. Results Phys. 26, 104357 (2021). https://doi.org/10.1016/J.RINP.2021.104357CrossRef

Zayed, E.M.E., Alngar, M.E.M.: Optical solitons in birefringent fibers with Biswas-Arshed model by generalized Jacobi elliptic function expansion method. Optik (Stuttg). 203, 163922 (2020). https://doi.org/10.1016/J.IJLEO.2019.163922ADSCrossRef

Title: Generalized periodic and soliton optical ultrashort pulses for perturbed Fokas–Lenells equation
Authors: Mahmoud Gaballah
Rehab M. El-Shiekh
Heba Hamdy
Publication date: 01-04-2023
Publisher: Springer US
Published in: Optical and Quantum Electronics / Issue 4/2023
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-023-04644-9

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