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Study of the parametric effects on soliton propagation in optical fibers through two analytical methods

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Abstract

The dual-core optical fiber has significant applications in optical electronics for long-wave propagation, especially in telecommunication fibers. The aim of this article is to study the parametric effects on solitary wave propagation and characteristic aspects of long-wave traveling through optical fibers by establishing some standard and wide-spectrum solutions via the improved Bernoulli sub-equation function (IBSEF) method and the new auxiliary equation (NAE) approach. The investigated solitary wave solutions are ascertained as an integration of hyperbolic, exponential, rational and trigonometric functions and can be extensively applicable in optics. The physical significance of the solutions attained is illustrated for the definite values of the included parameters through depicting the 3D profiles. The solitons profile represents different types of waves associated with the free parameters which are related to wave number and velocity. It turns out that the solutions obtained through both the methods are potential and can be used to interpret signals in telecommunication fibers and other works which can reduce casualties that ensue in essence.

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References

  • Abdelrahman, M.A.E., Moaaz, O.: New exact solutions to the dual-core optical fibers, Indian. J. Phys. 94, 705–711 (2020)

    Google Scholar 

  • Abdelrahman, A.E., Emad, H.M., Mostafa, M.A.: The exp(−ϕ(ξ)-expansion method and its application for solving nonlinear evolution equations Mahmoud. Int. J. Modern Nonlin. Theor. Appl. 4, 37–47 (2015)

    Article  Google Scholar 

  • Agrawa, G.P.: Applications of Nonlinear Fiber Optics. Academic Press, New York (1989)

    Google Scholar 

  • Agrawal, G.P.: Nonlinear fiber optics, 2nd edn. Academic Press, New York (2001)

    MATH  Google Scholar 

  • Akbar, M.A., Ali, N.H.M., Tanjim, T.: Outset of multiple soliton solutions to the nonlinear Schrödinger equation and the coupled Burgers equation. J. Phys. Commun. 3, 095013 (2019)

    Article  Google Scholar 

  • Ali, K.K., Cattani, C., Gómez-Aguilar, J.F., Baleanu, D., Osman, M.S.: Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model. Chaos Solitons Fract. 139, 110089 (2020)

    Article  MathSciNet  Google Scholar 

  • Barman, H.K., Aktar, M.S., Uddin, M.H., Akbar, M.A., Baleanu, D., Osman, M.S.: Physically significant wave solutions to the Riemann wave equations and the Landau-Ginsburg-Higgs equation. Results Phys. 27, 104517 (2021)

    Article  Google Scholar 

  • Baskonus, H.M., Sulaiman, T.A., Bulut, H.: Dark, bright and other optical solitons to the decoupled nonlinear Schrodinger equation arising in dual-core optical fibers. Opt. Quant. Electron 50, 165 (2018)

    Article  Google Scholar 

  • Baskonus, H.M., Bulut, H., Sulaiman, T.A.: New complex hyperbolic structures to the Lonngren wave equation by using sine-Gordon expansion method. Appl. Math. Nonlin. Sci. 4(1), 129–138 (2019)

    MathSciNet  Google Scholar 

  • Chen, Y.Q., Tang, Y.H., Manafian, J., Rezazadeh, H., Osman, M.S.: Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model. Nonlinear Dyn (2021). https://doi.org/10.1007/s11071-021-06642-6. (in press)

    Article  Google Scholar 

  • Chiang, K.S.: Intermodal dispersion in two-core optical fibers. Opt. Lett. 20, 997 (1992)

    Article  ADS  Google Scholar 

  • Chu, Y.-M., Md. Fahim, R.A., Kundu, P.R., Islam, M.E., Akbar, M.A., Inc, M.: Extension of the sine-Gordon expansion scheme and parametric effect analysis for higher-dimensional nonlinear evolution equations. J. King Saud Univ.-Sci., 33, 101515 (2021)

  • Ding, Y., Osman, M.S., Wazwaz, A.M.: Abundant complex wave solutions for the nonautonomous Fokas-Lenells equation in presence of perturbation terms. Optik- Int. J. Light Electron Optics 181, 503–513 (2019)

    Article  Google Scholar 

  • Helal, M.A., Seadawy, A.R., Zekry, M.H.: Stability analysis of solitary wave solutions for the fourth-order nonlinear Boussinesq water wave equation. Appl. Math. Comput. 232, 1094–1103 (2014)

    MathSciNet  MATH  Google Scholar 

  • Hosseini, K., Aligoli, M., Mirzazadeh, M., Eslami, M., Gómez-Aguilar, J.F.: Dynamics of rational solutions in a new generalized Kadomtsev-Petviashvili equation. Modern Phys. Lett. B 33(35), 1950437 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  • Hosseini, K., Osman, M.S., Mirzazadeh, M., Rabiei, F.: Investigation of different wave structures to the generalized third-order nonlinear Schrödinger equation. Optik-Int. J. Light Elect. Optics 206, 164259 (2020)

    Article  Google Scholar 

  • Iqbal, M., Seadawy, A.R., Khalil, O.H., Lu, D.: Propagation of long internal waves in density stratified ocean for the (2+1)-dimensional nonlinear Nizhnik-Novikov-Vesselov dynamical equation. Results Phys. 16, 102838 (2020)

    Article  Google Scholar 

  • Islam, M.E., Akbar, M.A.: Stable wave solutions to the Landau-Ginzburg-Higgs equation and the modified equal width wave equation using the IBSEF method. Arab J. Basic Appl. Sci. 27(1), 270–278 (2020a)

    Article  Google Scholar 

  • Islam, M.E., Akbar, M.A.: Stable wave solutions to the Landau-Ginzburg- Higgs equation and the modified equal width wave equation using the IBSEF method. Arab J. Basic Appl. Sci. 27(1), 270–278 (2020b)

    Article  Google Scholar 

  • Islam, M.E., Barman, H.K., Akbar, M.A.: Search for interactions of phenomena described by coupled Higgs field equation trough analytical solutions. Opt. Quant. Electron. 52(11), 1–19 (2020)

    Article  Google Scholar 

  • Islam, M.E., Akbar, M.A., Islam, M.T.: Searching closed form analytic solutions to some nonlinear fractional wave equations. Arab J. Basic Appl. Sci. 28(1), 64–72 (2021a)

    Article  Google Scholar 

  • Islam, M.E., Kundu, P.R., Akbar, M.A., Gepreel, K.A., Alotaibi, H.: Study of the parametric effect of self-control waves of the Nizhnik-Novikov-Veselov equation by the analytical solutions. Res. Phys. 22, 103887 (2021b)

    Google Scholar 

  • Kayum, M.A., Roy, R., Akbar, M.A., Osman, M.S.: Study of W-shaped, V-shaped, and other type of surfaces of the ZK-BBM and GZD-BBM equations. Opt. Quant. Electron 53, 387 (2021)

    Article  Google Scholar 

  • Khan, K., Akbar, M.A.: Exact and solitary wave solutions for the Tzitzeica-Dodd-Bullough and the modified KdV-Zakharov-Kuznetsov equations using the modified simple equation method. Ain Shams Engg. J. 4, 903–909 (2013a)

    Article  Google Scholar 

  • Khan, K., Akbar, M.A.: Travelling wave solutions of some coupled nonlinear evolution equations. ISRN Mathematical Physics 2013, 8 (2013b)

    MATH  Google Scholar 

  • Khater, M.M.A., Lu, D.C., Attia, R.A.M., Inç, M.: Analytical and approximate solutions for complex nonlinear Schrödinger equation via generalized auxiliary equation and numerical schemes. Commun. Theo. Phys. 71(11), 1267 (2019)

    Article  ADS  Google Scholar 

  • Kudryashov, N.A.: Exact solutions of the equation for surface waves in a convecting fluid. Appl. Math. Comput. 344(345), 97–106 (2019)

    MathSciNet  MATH  Google Scholar 

  • Kumar, S., Niwas, M., Osman, M. S. and Abdou, M. Abundant different types of exact-soliton solutions to the (4+1)-dimensional Fokas and (2+1)-dimensional Breaking soliton equations. Commun. Theor. Phys. (2021). https://doi.org/10.1088/1572-9494/ac11ee

  • Kundu, P.R., Almusawa, H., Fahim, M.R.A., Islam, M.E., Akbar, M.A., Osman, M.S.: Linear and nonlinear effects analysis on wave profiles in optics and quantum physics. Results Phys. 23, 103995 (2021)

    Article  Google Scholar 

  • Li, J., Qui, Y., Lu, D., Attia, R.A.M., Khater, M.M.A.: Study on the solitary wave solutions of the ionic currents on microtubules equation by using the modified Khater method. Thermal Sci. 23(Suppl. 6), 2053–2062 (2019)

    Article  Google Scholar 

  • Malik, S., Almusawa, H., Kumar, S., Wazwaz, A.M., Osman, M.S.: A (2+1)-dimensional Kadomtsev-Petviashvili equation with competing dispersion effect: Painlevé analysis, dynamical behavior and invariant solutions. Res. Phys. 23, 104043 (2021)

    Google Scholar 

  • Mirzazadeh, M., Eslami, M., Zerrad, E., Mahmood, M.F., Biswas, A., Belic, M.: Optical solitons in nonlinear directional couplers by sine-cosine function method and Bernoulli’s equation approach. Nonlin. Dyn. 81(4), 1933–1949 (2015)

    Article  MathSciNet  Google Scholar 

  • Nair, A.A., Porsezian, K., Jayaraju, M.: Impact of higher order dispersion and nonlinearities on modulational instability in a dual-core optical fiber. Eur. Phys. J. D 72, 6 (2018)

    Article  ADS  Google Scholar 

  • Osman, M.S.: Analytical study of rational and double-soliton rational solutions governed by the KdV-Sawada-Kotera-Ramani equation with variable coefficients. Nonlinear Dyn. 89(11), 1–7 (2017)

    MathSciNet  Google Scholar 

  • Osman, M.S., Ali, K.K.: Optical soliton solutions of perturbing time-fractional nonlinear Schrödinger equations. Optik- Int. J. Light Electron Optics 209, 164589 (2020)

    Article  Google Scholar 

  • Raza, N., Osman, M.S., Abdel-Aty, A.H., Abdel-Khalek, S., Babes, H.R.: Optical solitons of space-time fractional Fokas-Lenells equation with two versatile integration architectures. Adv. Differ. Equn. 2020(517), 1–15 (2020)

    MathSciNet  Google Scholar 

  • Shamseldeen, S., Latif, M.S.A., Hamed, A., Nour, H.: New soliton solutions in dual-core optical fibers. Commun. Math. Modeling Appl. CMMA 2(2), 39–46 (2017)

    Google Scholar 

  • Tahir, M., Kumar, S., Rehman, H., Ramzan, M., Hasan, A., Osman, M.S.: Exact traveling wave solutions of Chaffee-Infante equation in (2+1)-dimensions and dimensionless Zakharov equation. Math. Met. Appl. Sci. 40(2), 1500–1513 (2021)

    Article  MathSciNet  Google Scholar 

  • Yépez-Martíneza, H., Gómez-Aguilarb, 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)

    Article  ADS  Google Scholar 

  • Yokus, A., Baskonus, H.M., Sulaiman, T.A., Bulut, H.: Numerical simulation and solutions of the two-component second order KdV evolutionary system. Numer. Meth. Partial Diff. Eqn. 34(1), 211–227 (2018)

    Article  MathSciNet  Google Scholar 

  • Younis, M., Rizvi, S.T.R., Zhou, Q., Biswas, A., Belic, M.: Optical solitons in dual-core fibers with (G’G)-expansion scheme. J. Optoelectronics Adv. Mater. 17(3–4), 505–510 (2015)

    Google Scholar 

  • Zhang, L.D., Tian, S.F., Peng, W.Q., Zhang, T.T., Yan, X.J.: The dynamics of lump, Lumpoff and Rogue wave Solutions of (2+1)-DIMENSIONAL Hirota-Satsuma-Ito equations. East Asian J. Appl. Math. 10(2), 243–255 (2020)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work is supported by the Research Grant No.: A-1220/5/52/RU/Science-37/2019-2020 and the authors acknowledge this support. The authors would like to thank the anonymous referee for his insightful comments and ideas for improving the article.

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Authors and Affiliations

  1. Department of Mathematics, Pabna University of Science and Technology, Pabna, Bangladesh

    Md. Ekramul Islam

  2. Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh

    M. Ali Akbar

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  1. Md. Ekramul Islam
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  2. M. Ali Akbar
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Correspondence to M. Ali Akbar.

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Islam, M.E., Akbar, M.A. Study of the parametric effects on soliton propagation in optical fibers through two analytical methods. Opt Quant Electron 53, 585 (2021). https://doi.org/10.1007/s11082-021-03234-x

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