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Optical and Quantum Electronics

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01-04-2023

Optical solitons to time-fractional Sasa-Satsuma higher-order non-linear Schrödinger equation via three analytical techniques

Authors: M. Raheel, Asim Zafar, Mustafa Inc, E. Tala-Tebue

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

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Abstract

This current research is about the exact solitons of time-fractional Sasa-Satsuma higher order non-linear Schrödinger equation with novel definition of derivative that are achieved with the use of three analytical methods i.e extended Jacobi’s elliptic expansion function method (EJEEFM), \(\exp _a\) function method and Kudryashov method. The obtained optical solitons are verified with the use of Mathematica software. Finally, different graphs are also drawn of the gained solutions. The main purpose of our work is to explain the effect of beta-time fractional derivative on the solutions of Sasa-Satsuma equation that are gained with the use of EJEEF, \(\exp _a\) function, Kudryashov methods. These exact solitons show that these three techniques are efficient, simple and reliable than other techniques.

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Abdou, M.A., Elhanbaly, A.: Construction of periodic and solitary wave solutions by the extended Jacobi elliptic function expansion method. Commun. Nonlinear Sci. Numer. Sim. 12, 1229–1241 (2007)MathSciNetCrossRefMATH

Akinyemi, L., Inc, M., Khater, M.M.A., Rezazadeh, H.: Dynamical behaviour of chiral nonlinear Schrödinger equation. Optic. Quantum Electron. 54, 191 (2022)CrossRef

Akinyemi, L., Veeresha, P., Darvishi, M.T., Rezazadeh, H., Senol, M., Akpan, U.: A novel approach to study generalized coupled cubic Schrödinger-Korteweg-de Vries equations. J. Ocean Eng. Sci. (2022a). https://doi.org/10.1016/j.joes.2022.06.004

Akinyemi, L., Akpan, U., Veeresha, P., Rezazadeh, H., Inc, M.: Computational techniques to study the dynamics of generalized unstable nonlinear Schrödinger equation. J. Ocean Eng. Sci. (2022b). https://doi.org/10.1016/j.joes.2022.02.011

Ali, A.T., Hassan, E.R.: General \(Exp_a\)-function method for nonlinear evolution equations. Appl. Math. Comput. 217, 451–459 (2010)MathSciNet

Atangana, A., Alqahtani, R.T.: Modelling the spread of river blindness disease via the Caputo fractional derivative and the beta-derivative. Entropy 18, 40 (2016)CrossRefADS

Atangana, A., Baleanu, D., Alsaedi, A.: Analysis of time-fractional Hunter-Saxton equation: a model of neumatic liquid crystal. Open Phys. 14, 145–149 (2016)CrossRef

Bekir, A.: Application of the extended tanh method for coupled nonlinear evolution equation. Commun. Nonlinear Sci. Numer. Sim. 13, 1742–1751 (2008)MathSciNet

Ghanbari, B., Gómez-Aguilar, J.F.: The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with Beta time derivative. Revista Mexicana de Física 65, 503–518 (2019)MathSciNetCrossRef

Gonzalez-Gaxiola, O., Biswas, A., Ekici, M., Alshomrani, A.S.: Optical solitons with Sasa-Satsuma equation by Laplace-Adomian decomposition algorithm. Optik 229, 166262 (2021)CrossRefADS

Hosseini, K., Ayati, Z.: Exact solutions of space-time fractional EW and modified EW equations using Kudryashov method. Nonlinear Sci. Lett. A 7, 58–66 (2016)

Hosseini, K., Ayati, Z., Ansari, R.: New exact solutions of the Tzitzéica-type equations in non-linear optics using the \(exp_a\) function method. J. Mod. Opt. 65(7), 847–851 (2018a)

Hosseini, K., Zabihi, A., Samadani, F., Ansari, R.: New explicit exact solutions of the unstable nonlinear Schrödinger’s equation using the \(exp_a\) and hyperbolic function methods. Opt. Quantum Electron. 50, 82 (2018b)

Hosseini, K., Mirzazadeh, M., Ilie, M., Radmehr, S.: Dynamics of optical solitons in the perturbed Gerdjikov-Ivanov equation. Optik 206, 164350 (2020)CrossRefADS

Hosseini, K., Mirzazadeh, M., Ilie, M., Gomez-Aguilar, J.F.: Biswas-Arshed equation with the beta time derivative: Optical solitons and other solutions. Optik 217, 164801 (2020)CrossRefADS

Huiqun, Z.: Extended Jacobi elliptic function expansion method and its applications. Commun. Nonlinear Sci. Numer. Sim. 12, 627–635 (2007)MathSciNetCrossRefMATH

Inan, I.E., Inc, M., Rezazadeh, H., Akinyemi, L.: Optical solitons of (3+ 1) dimensional and coupled nonlinearSchrödinger equations. Optic. Quantum Electron. 54, 261 (2022)CrossRef

Khodadad, F.S., Alizamini, S.M.M., Günay, B., Akinyemi, L., Rezazadeh, H., Inc, M.: Abundant optical solitons to the Sasa Satsuma higher order nonlinear Schrödinger equation. Optic. Quantum Electron. 53(12), 1–17 (2021)

Kudryashov, N.A.: Method for finding highly dispersive optical solitons of nonlinear differential equation. Optik 206, 163550 (2019)CrossRefADS

Li, C., Chen, L., Li, G.: Optical solitons of space-time fractional Sasa-Satsuma equation by F-expansion method. Optik 224, 165527 (2020)CrossRefADS

Manafian, J.: Optical soliton solutions for Schrodinger type nonlinear evolution equations by the \(tan(\phi /2)\)-expansion method. Optik 127(10), 4222–4245 (2016)CrossRefADS

Mirzazadeh, M., Akbulut, A., Taşcan, F., Akinyemi, L.: A novel integration approach to study the perturbed Biswas-Milovic equation with Kudryashov’s law of refractive index. Optik 252, 168529 (2022)CrossRefADS

Uddin, M.F., Hafez, M.G., Hammouch, Z., Baleanu, D.: Periodic and rogue waves for Heisenberg models of ferromagnetic spin chains with fractional beta derivative evolution and obliqueness. Waves Random Complex Med. 31, 2135–2149 (2021)MathSciNetCrossRefMATHADS

Wazwaz, A.M.: A study on linear and nonlinear Schrodinger equations by the variational iteration method. Chaos Solitons Fractals 37(4), 1136–1142 (2008)MathSciNetCrossRefMATHADS

Wazwaz, A.M., Mehanna, M.: Higher-order Sasa-Satsuma equation: bright and dark optical solitons. Optik 243, 167421 (2021)CrossRefADS

Yao, S.W., Akinyemi, L., Mirzazadeh, M., Inc, M., Hosseini, K., Senol, M.: Dynamics of optical solitons in higher-order Sasa-Satsuma equation. Results Phys. 30, 104825 (2021)CrossRef

Yépez-Martínez, H., Gómez-Aguilar, J.F., Baleanu, D.: Beta-derivative and sub-equation method applied to the optical solitons in medium with parabolic law nonlinearity and higher order dispersion. Optik 155, 357–365 (2018)CrossRefADS

Yıldırım, Y.: Optical solitons to Sasa-Satsuma model with trial equation approach. Optik 184, 70–74 (2019)CrossRefADS

Yıldırım, Y.: Optical solitons to Sasa-Satsuma model with modified simple equation approach. Optik 184, 271–276 (2019)CrossRefADS

Yusuf, A., Inc, M., Aliyu, A.I., Baleanu, D.: Optical solitons possessing beta derivative of the Chen- Lee-Liu equation in optical fibers. Front. Phys. 7, 34 (2019)CrossRef

Zafar, A.: The \(exp_a\) function method and the conformable time-fractional KdV equations. Nonlinear Eng. 8, 728–732 (2019)CrossRefADS

Zafar, A., Bekir, A., Raheel, M., Rezazadeh, H.: Investigation for optical soliton solutions of two nonlinear Schrödinger equations via two concrete finite series methods. Int. J. Appl. Comput. Math. 6, 1–13 (2020)CrossRefMATH

Zafar, A., Raheel, M., Bekir, A.: Expolring the dark and singular soliton solutions of Biswas-Arshed model with full nonlinear form. Optik 204, 164133 (2020)CrossRefADS

Zafar, A., Raheel, M., Asif, M., Hosseini, K., Mirzazadeh, M., Akinyemi, L.: Some novel integration techniques to explore the conformable M-fractional Schrödinger-Hirota equation. J. Ocean Eng. Sci. 7, 337–344 (2022)CrossRef

Zayed, E.M.E., Al-Nowehy, A.G.: Generalized kudryashov method and general \(exp_a\) function method for solving a high order nonlinear schrödinger equation. J. Space Explor. 6, 1–26 (2017)

Zhang, W.: Extended Jacobi elliptic function expansion method to the ZK-MEW equation. Int. J. Differ. Equ. 2011, 451420 (2011)MathSciNetMATH

Zhou, Q., Biswas, A.: Optical soliton in parity-time-symmetric mixed linear and nonlinear lattice with non-Kerr law nonlinearity. Superlatices Microstruct 109, 588–598 (2017)CrossRefADS

Title: Optical solitons to time-fractional Sasa-Satsuma higher-order non-linear Schrödinger equation via three analytical techniques
Authors: M. Raheel
Asim Zafar
Mustafa Inc
E. Tala-Tebue
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/s11082-023-04565-7

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