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Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method

Author

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  • Noha M. Rasheed

    (Department of Basic Sciences, Al-Huson University College, Balqa Applied University, Al-Huson 21510, Jordan)

  • Mohammed O. Al-Amr

    (Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul 41002, Iraq)

  • Emad A. Az-Zo’bi

    (Department of Mathematics and Statistics, Faculty of Science, Mutah University, AlKarak 61710, Jordan)

  • Mohammad A. Tashtoush

    (Department of Basic Sciences, Al-Huson University College, Balqa Applied University, Al-Huson 21510, Jordan)

  • Lanre Akinyemi

    (Department of Mathematics, Lafayette College, Easton, PA 18042, USA)

Abstract

This paper studies the propagation of the short pulse optics model governed by the higher-order nonlinear Schrödinger equation (NLSE) with non-Kerr nonlinearity. Exact one-soliton solutions are derived for a generalized case of the NLSE with the aid of software symbolic computations. The modified Kudryashov simple equation method (MSEM) is employed for this purpose under some parametric constraints. The computational work shows the difference, effectiveness, reliability, and power of the considered scheme. This method can treat several complex higher-order NLSEs that arise in mathematical physics. Graphical illustrations of some obtained solitons are presented.

Suggested Citation

  • Noha M. Rasheed & Mohammed O. Al-Amr & Emad A. Az-Zo’bi & Mohammad A. Tashtoush & Lanre Akinyemi, 2021. "Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method," Mathematics, MDPI, vol. 9(16), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1986-:d:617782
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    References listed on IDEAS

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    1. Alvaro H. Salas & Lorenzo J. Martinez H & David L. Ocampo R, 2021. "New Solutions for the Generalized BBM Equation in terms of Jacobi and Weierstrass Elliptic Functions," Abstract and Applied Analysis, Hindawi, vol. 2021, pages 1-10, April.
    2. Akinyemi, Lanre & Şenol, Mehmet & Iyiola, Olaniyi S., 2021. "Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 211-233.
    3. Kudryashov, Nikolai A., 2005. "Simplest equation method to look for exact solutions of nonlinear differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1217-1231.
    4. Pellegrino, E. & Pezza, L. & Pitolli, F., 2020. "A collocation method in spline spaces for the solution of linear fractional dynamical systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 266-278.
    5. Az-Zo'bi, Emad A. & Dawoud, Kamal Al & Marashdeh, Mohammad, 2015. "Numeric-analytic solutions of mixed-type systems of balance laws," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 133-143.
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    Cited by:

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