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Optical and Quantum Electronics

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01.05.2024

Hirota–Maccari system arises in single-mode fibers: abundant optical solutions via the modified auxiliary equation method

verfasst von: Hajar F. Ismael, Haci Mehmet Baskonus, Azad Piro Shakir

Erschienen in: Optical and Quantum Electronics | Ausgabe 5/2024

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Abstract

This research paper’s primary goal is to find fresh approaches to the Hirota–Maccari system. This system explains the dynamical features of the femto-second soliton pulse in single-mode fibers. The bright soliton, dark soliton, dark-bright soliton, dark singular, bright singular, periodic soliton, and singular solutions are developed utilizing the modified auxiliary equation technique. To make the physical significance of each unique solution clearer, it is mapped in both 2D and 3D. The primary Hirota–Maccari system is being verified by all new solutions, and the constraint condition is also provided. The obtained optical solitons may be important for the analysis of nonlinear processes in optic fiber communication and signal processing.

Vorheriger Artikel High-q resonances in silicon nanoparticle coupled to nanopit

Nächster Artikel Dynamic study of qualitative analysis, traveling waves, solitons, bifurcation, quasiperiodic, and chaotic behavior of integrable kuralay equations

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Akram, G., et al.: Abundant solitary wave solutions of Gardner’s equation using three effective integration techniques. AIMS Math. 8(4), 8171–8184 (2023)MathSciNetCrossRef

Akram, G., Sajid, N.: The investigation of exact solutions of Korteweg-de vries equation with dual power law nonlinearity using the \(\exp _a\) and \(\exp (-\Phi (\xi ))\) methods. Int. J. Comput. Math. 99(3), 629–640 (2022)

Akram, G., Sadaf, M., Sarfraz, M., Anum, N.: Dynamics investigation of (1+ 1)-dimensional time-fractional potential Korteweg-de Vries equation. Alex. Eng. J. 61(1), 501–509 (2022a)CrossRef

Akram, G., Sadaf, M., Khan, M.A.U.: Abundant optical solitons for Lakshmanan–Porsezian–Daniel model by the modified auxiliary equation method. Optik 251, 168163 (2022b)ADSCrossRef

Akram, G., Sadaf, M., Khan, M.A.U.: Soliton solutions of Lakshmanan–Porsezian–Daniel model using modified auxiliary equation method with parabolic and anti-cubic law of nonlinearities. Optik 252, 168372 (2022c)ADSCrossRef

Akram, G., Sadaf, M., Zainab, I.: New graphical observations for KdV equation and KdV-Burgers equation using modified auxiliary equation method. Mod. Phys. Lett. B 36(01), 2150520 (2022d)ADSMathSciNetCrossRef

Ali, K.K., Yokus, A., Seadawy, A.R., Yilmazer, R.: The ion sound and Langmuir waves dynamical system via computational modified generalized exponential rational function. Chaos Solitons Fractals 161, 112381 (2022)MathSciNetCrossRef

AL-Jawary, M.A., Radhi, G.H., Ravnik, J.: Daftardar–Jafari method for solving nonlinear thin film flow problem. Arab. J. Basic Appl. Sci. 25, 20–27 (2018)CrossRef

Alquran, M.: New interesting optical solutions to the quadratic–cubic Schrodinger equation by using the Kudryashov-expansion method and the updated rational sine–cosine functions. Opt. Quantum Electron. 54(10), 666 (2022)CrossRef

Alquran, M.: Classification of single-wave and bi-wave motion through fourth-order equations generated from the Ito model. Phys. Scr. 98(8), 085207 (2023)ADSCrossRef

Alquran, M., Alhami, R.: Analysis of lumps, single-stripe, breather-wave, and two-wave solutions to the generalized perturbed-KdV equation by means of Hirota’s bilinear method. Nonlinear Dyn. 109(3), 1985–1992 (2022)CrossRef

Alquran, M., Ali, M., Jadallah, H.: New topological and non-topological unidirectional-wave solutions for the modified-mixed KdV equation and bidirectional-waves solutions for the Benjamin Ono equation using recent techniques. J. Ocean Eng. Sci. 7(2), 163–169 (2022)CrossRef

Alquran, M., Najadat, O., Ali, M., Qureshi, S.: New kink-periodic and convex–concave-periodic solutions to the modified regularized long wave equation by means of modified rational trigonometric–hyperbolic functions. Nonlinear Eng. 12(1), 20220307 (2023)ADSCrossRef

Alquran, M., Ali, M., Gharaibeh, F., Qureshi, S.: Novel investigations of dual-wave solutions to the Kadomtsev–Petviashvili model involving second-order temporal and spatial-temporal dispersion terms. Partial Differ. Equ. Appl. Math. 8, 100543 (2023)CrossRef

Aminikhah, H., Refahi Sheikhani, A.H., Rezazadeh, H.: Sub-equation method for the fractional regularized long-wave equations with conformable fractional derivatives. Sci. Iran. (2017). CrossRef

Arshad, M., Seadawy, A.R., Lu, D.: Exact bright–dark solitary wave solutions of the higher-order cubic–quintic nonlinear Schrödinger equation and its stability. Optik (2017). ADSCrossRef

Baskonus, H.M., Bulut, H.: On the numerical solutions of some fractional ordinary differential equations by fractional Adams–Bashforth–Moulton method. Open Math. (2015). https://doi.org/10.1515/math-2015-0052MathSciNetCrossRef

Baskonus, H.M., Bulut, H.: Exponential prototype structures for (2+1)-dimensional Boiti–Leon–Pempinelli systems in mathematical physics. Waves Random Complex Med. (2016). https://doi.org/10.1080/17455030.2015.1132860ADSMathSciNetCrossRef

Baskonus, H.M., Sulaiman, T.A., Bulut, H.: On the novel wave behaviors to the coupled nonlinear Maccari’s system with complex structure. Optik (2017). https://doi.org/10.1016/j.ijleo.2016.10.135ADSCrossRef

Bilal, M., Haris, H., Waheed, A., Faheem, M.: The analysis of exact solitons solutions in monomode optical fibers to the generalized nonlinear Schrödinger system by the compatible techniques. Int. J. Math. Comput. Eng. 1, 149–170 (2023)CrossRef

Bulut, H., Baskonus, H.M., Pandir, Y.: The modified trial equation method for fractional wave equation and time fractional generalized burgers equation. Abstr. Appl. Anal. (2013). https://doi.org/10.1155/2013/636802

Cao, F., Lü, X., Zhou, Y.-X., Cheng, X.-Y.: Modified SEIAR infectious disease model for Omicron variants spread dynamics. Nonlinear Dyn. 111, 14597–14620 (2023)CrossRef

Cattani, C., Sulaiman, T.A., Baskonus, H.M., Bulut, H.: Solitons in an inhomogeneous Murnaghan’s rod. Eur. Phys. J. Plus (2018). https://doi.org/10.1140/epjp/i2018-12085-yCrossRef

Chen, Y., Lü, X.: Wronskian solutions and linear superposition of rational solutions to B-type Kadomtsev–Petviashvili equation. Phys. Fluids 35(10), 106613 (2023)ADSCrossRef

Chen, Y., Lü, X., Wang, X.-L.: Bäcklund transformation, Wronskian solutions and interaction solutions to the (3+ 1)-dimensional generalized breaking soliton equation. Eur. Phys. J. Plus 138(6), 492 (2023)CrossRef

Chen, S.-J., Yin, Y.-H., Lü, X.: Elastic collision between one lump wave and multiple stripe waves of nonlinear evolution equations. Commun. Nonlinear Sci. Numer. Simul. 130, 107205 (2024)MathSciNetCrossRef

Dewasurendra, M., Vajravelu, K.: On the method of inverse mapping for solutions of coupled systems of nonlinear differential equations arising in nanofluid flow, heat and mass transfer. Appl. Math. Nonlinear Sci. 20, 3 (2018). https://doi.org/10.21042/amns.2018.1.00001MathSciNetCrossRef

El-Borai, M.M., El-Owaidy, H.M., Ahmed, H.M., Arnous, A.H.: Soliton solutions of Hirota equation and Hirota–Maccari system. New Trends Math. Sci. 4(3), 231–238 (2016)MathSciNetCrossRef

Eslami, M., Rezazadeh, H.: The first integral method for Wu–Zhang system with conformable time-fractional derivative. Calcolo (2016). https://doi.org/10.1007/s10092-015-0158-8MathSciNetCrossRef

Gao, W., Ismael, H.F., Husien, A.M., Bulut, H., Baskonus, H.M.: Optical soliton solutions of the cubic–quartic nonlinear Schrödinger and resonant nonlinear Schrödinger equation with the parabolic law. Appl. Sci. 10(1), 219 (2019). https://doi.org/10.3390/app10010219CrossRef

Gao, D., Lü, X., Peng, M.-S.: Study on the (2+ 1)-dimensional extension of Hietarinta equation: soliton solutions and Bäcklund transformation. Phys. Scr. 98(9), 95225 (2023)CrossRef

Ghanbari, B.: Abundant soliton solutions for the Hirota–Maccari equation via the generalized exponential rational function method. Mod. Phys. Lett. B (2019). https://doi.org/10.1142/s0217984919501069

Hammouch, Z., Mekkaoui, T.: Traveling-wave solutions of the generalized Zakharov equation with time-space fractional derivatives. J. MESA 5(4), 489–498 (2014)

Hammouch, Z., Mekkaoui, T., Agarwal, P.: Optical solitons for the Calogero–Bogoyavlenskii–Schiff equation in (2 + 1) dimensions with time-fractional conformable derivative. Eur. Phys. J. Plus (2018). https://doi.org/10.1140/epjp/i2018-12096-8CrossRef

Hirota, R.: Exact envelope-soliton solutions of a nonlinear wave equation. J. Math. Phys. 14(7), 805–809 (1973)ADSMathSciNetCrossRef

Hirota, R., Ito, M.: A direct approach to multi-periodic wave solutions to nonlinear evolution equations. J. Phys. Soc. Jpn. (1981). https://doi.org/10.1143/JPSJ.50.338ADSCrossRef

Hoseini, S.M., Marchant, T.R.: Soliton perturbation theory for a higher order Hirota equation. Math. Comput. Simul. 80(4), 770–778 (2009)MathSciNetCrossRef

Hussain, A., Ali, H., Zaman, F., Abbas, N.: New closed form solutions of some nonlinear pseudo-parabolic models via a new extended direct algebraic method. Int. J. Math. Comput. Eng. 1(2), 149–170 (2023)

Ilhan, O.A., Bulut, H., Sulaiman, T.A., Baskonus, H.M.: Dynamic of solitary wave solutions in some nonlinear pseudoparabolic models and Dodd–Bullough–Mikhailov equation. Indian J. Phys. (2018). https://doi.org/10.1007/s12648-018-1187-3ADSCrossRef

Ismael, H.F.: Carreau–Casson fluids flow and heat transfer over stretching plate with internal heat source/sink and radiation. Int. J. Adv. Appl. Sci. J. 6(2), 81–86 (2017). https://doi.org/10.1371/journal.pone.0002559CrossRef

Ismael, H.F., Ali, K.K.: MHD Casson flow over an unsteady stretching sheet. Adv. Appl. Fluid Mech. 20(4), 533–541 (2017). https://doi.org/10.17654/FM020040533CrossRef

Ismael, H.F., Arifin, N.M.: Flow and heat transfer in a Maxwell liquid sheet over a stretching surface with thermal radiation and viscous dissipation. JP J. Heat Mass Transf. 15(4), 847–866 (2018). https://doi.org/10.17654/HM015040847CrossRef

Ismael, H.F., Bulut, H., Baskonus, H.M.: Optical soliton solutions to the Fokas–Lenells equation via sine-Gordon expansion method and \((m+ ({G^{\prime }}/{G}))\)-expansion method. Pramana 94(1), 1–9 (2020)

Javeed, S., Hincal, E.: Solving coupled non-linear higher order BVPs using improved shooting method. Int. J. Math. Comput. Eng. 2(2), 25–38 (2024)

Kocak, Z.F., Bulut, H., Yel, G.: The solution of fractional wave equation by using modified trial equation method and homotopy analysis method. In: AIP Conference Proceedings, vol. 1637, no. 1, pp. 504–512 (2014). https://doi.org/10.1063/1.4904617

Li-Na, S., Hong-Qing, Z.: Extended Sine–Gordon equation method and its application to Maccari’s system. Commun. Theor. Phys. 44(5), 783 (2005)ADSMathSciNetCrossRef

Liu, K., Lü, X., Gao, F., Zhang, J.: Expectation-maximizing network reconstruction and most applicable network types based on binary time series data. Phys. D Nonlinear Phenom. 454, 133834 (2023)MathSciNetCrossRef

Lu, D., Seadawy, A., Arshad, M.: Applications of extended simple equation method on unstable nonlinear Schrödinger equations. Optik (2017). https://doi.org/10.1016/j.ijleo.2017.04.032ADSCrossRef

Maccari, A.: A generalized Hirota equation in 2+1 dimensions. J. Math. Phys. 39(12), 6547–6551 (1998)ADSMathSciNetCrossRef

Oruç, Ö., Bulut, F., Esen, A.: Numerical solution of the KdV equation by Haar wavelet method. Pramana 87(6), 94 (2016)ADSCrossRef

Osman, M.S., Ghanbari, B.: New optical solitary wave solutions of Fokas–Lenells equation in presence of perturbation terms by a novel approach. Optik (2018). https://doi.org/10.1016/j.ijleo.2018.08.007ADSCrossRef

Sadaf, M., Akram, G., Dawood, M.: An investigation of fractional complex Ginzburg–Landau equation with Kerr law nonlinearity in the sense of conformable, beta and M-truncated derivatives. Opt. Quantum Electron. 54(4), 248 (2022)CrossRef

Sulaiman, T.A., Yel, G., Bulut, H.: M-fractional solitons and periodic wave solutions to the Hirota–Maccari system. Mod. Phys. Lett. B 1950052 (2019). https://doi.org/10.1142/s0217984919500520

Sulaiman, T.A., Bulut, H., Yokus, A., Baskonus, H.M.: On the exact and numerical solutions to the coupled Boussinesq equation arising in ocean engineering. Indian J. Phys. (2019). https://doi.org/10.1007/s12648-018-1322-1ADSCrossRef

Tariq, H., et al.: Computational study for the conformable nonlinear Schrödinger equation with cubic–quintic–septic nonlinearities. Results Phys. 30, 104839 (2021)CrossRef

Tarla, S., Ali, K.K., Yilmazer, R., Yusuf, A.: Investigation of the dynamical behavior of the Hirota–Maccari system in single-mode fibers. Opt. Quantum Electron. 54(10), 613 (2022)CrossRef

Vakhnenko, V.O., Parkes, E.J., Morrison, A.J.: A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation. Chaos Solitons Fractals (2003). https://doi.org/10.1016/S0960-0779(02)00483-6ADSMathSciNetCrossRef

Wang, M., Li, X.: Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation. Chaos Solitons Fractals (2005). https://doi.org/10.1016/j.chaos.2004.09.044ADSMathSciNetCrossRef

Wazwaz, A.-M.: Abundant soliton and periodic wave solutions for the coupled Higgs field equation, the Maccari system and the Hirota–Maccari system. Phys. Scr. 85(6), 65011 (2012)CrossRef

Yang, X., Yang, Y., Cattani, C., Zhu, C.M.: A new technique for solving the 1-D Burgers equation. Therm. Sci. (2017). https://doi.org/10.2298/TSCI17S1129YCrossRef

Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified PINNs: soliton solutions, rogue waves and parameter discovery of the CQ-NLSE. Commun. Nonlinear Sci. Numer. Simul. 126, 107441 (2023)MathSciNetCrossRef

Yin, Y.-H., Lü, X., Jiang, R., Jia, B., Gao, Z.: Kinetic analysis and numerical tests of an adaptive car-following model for real-time traffic in ITS. Phys. A Stat. Mech. Appl. 635, 129494 (2024)MathSciNetCrossRef

Yousif, M.A., Mahmood, B.A., Ali, K.K., Ismael, H.F.: Numerical simulation using the homotopy perturbation method for a thin liquid film over an unsteady stretching sheet. Int. J. Pure Appl. Math. 107(2), 289–300 (2016). https://doi.org/10.12732/ijpam.v107i2.1CrossRef

Zhang, S.: Exp-function method for solving Maccari’s system. Phys. Lett. A 371(1–2), 65–71 (2007)ADSCrossRef

Titel: Hirota–Maccari system arises in single-mode fibers: abundant optical solutions via the modified auxiliary equation method
verfasst von: Hajar F. Ismael
Haci Mehmet Baskonus
Azad Piro Shakir
Publikationsdatum: 01.05.2024
Verlag: Springer US
Erschienen in: Optical and Quantum Electronics / Ausgabe 5/2024
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-024-06698-9

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