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Highly Dispersive Optical Solitons in Birefringent Fibers with Polynomial Law of Nonlinear Refractive Index by Laplace–Adomian Decomposition

Author

Listed:
  • Oswaldo González-Gaxiola

    (Applied Mathematics and Systems Department, Universidad Autónoma Metropolitana-Cuajimalpa, Vasco de Quiroga 4871, Mexico City 05348, Mexico)

  • Anjan Biswas

    (Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Hwy, 115409 Moscow, Russia
    Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Applied Sciences, Cross–Border Faculty, Dunarea de Jos University of Galati, 111 Domneasca Street, 800201 Galati, Romania
    Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, South Africa)

  • Yakup Yıldırım

    (Department of Mathematics, Faculty of Arts and Sciences, Near East University, Nicosia 99138, Cyprus)

  • Luminita Moraru

    (Department of Chemistry, Physics and Environment, Faculty of Sciences and Environment, Dunarea de Jos University of Galati, 47 Domneasca Street, 800008 Galati, Romania
    The Modelling & Simulation Laboratory, Dunarea de Jos University of Galati, 47 Domneasca Street, 800008 Galati, Romania)

Abstract

This paper is a numerical simulation of highly dispersive optical solitons in birefringent fibers with polynomial nonlinear form, which is achieved for the first time. The algorithmic approach is applied with the usage of the Laplace–Adomian decomposition scheme. Dark and bright soliton simulations are presented. The error measure has a very low count, and thus, the simulations are almost an exact replica of such solitons that analytically arise from the governing system. The suggested iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions.

Suggested Citation

  • Oswaldo González-Gaxiola & Anjan Biswas & Yakup Yıldırım & Luminita Moraru, 2022. "Highly Dispersive Optical Solitons in Birefringent Fibers with Polynomial Law of Nonlinear Refractive Index by Laplace–Adomian Decomposition," Mathematics, MDPI, vol. 10(9), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1589-:d:810743
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    References listed on IDEAS

    as
    1. Kudryashov, Nikolay A., 2020. "Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    2. Feng Wang & Yan-Cheng Liu & Hui Zheng, 2022. "A Localized Method of Fundamental Solution for Numerical Simulation of Nonlinear Heat Conduction," Mathematics, MDPI, vol. 10(5), pages 1-15, February.
    3. Kudryashov, Nikolay A., 2020. "Highly dispersive optical solitons of equation with various polynomial nonlinearity law," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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