2025 Volume 15 Issue 6
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M. Elsaid Ramadan, Hamdy M. Ahmed, Abeer S. Khalifa, Karim K. Ahmed. INVARIANT SOLITONS AND TRAVELLING-WAVE SOLUTIONS TO A HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION IN AN OPTICAL FIBER WITH AN IMPROVED TANH-FUNCTION ALGORITHM[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3270-3289. doi: 10.11948/20250042
Citation: M. Elsaid Ramadan, Hamdy M. Ahmed, Abeer S. Khalifa, Karim K. Ahmed. INVARIANT SOLITONS AND TRAVELLING-WAVE SOLUTIONS TO A HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION IN AN OPTICAL FIBER WITH AN IMPROVED TANH-FUNCTION ALGORITHM[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3270-3289. doi: 10.11948/20250042
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INVARIANT SOLITONS AND TRAVELLING-WAVE SOLUTIONS TO A HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION IN AN OPTICAL FIBER WITH AN IMPROVED TANH-FUNCTION ALGORITHM

  • 1.

    Department of Mathematics, Faculty of Science, Islamic University of Madinah, 42351 Medina, Saudi Arabia

  • 2.

    Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, 11837 Cairo, Egypt

  • 3.

    Department of Mathematics, Faculty of Basic Sciences, the German University in Cairo (GUC), 11835 Cairo, Egypt

  • 4.

    Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, Egypt

    Abstract

  • Optical fiber connection is essential to modern communication. A high-order nonlinear Schrödinger equation (NLSE) with additional dispersion of high-order and nonlinear components is studied in an inhomogeneous optical fiber. We provide numerous new analytic solutions via the improved modified extended tanh-function algorithm, including rational solution, singular periodic solution, Jacobi elliptic solutions (JESs), (bright, singular, dark) soliton, Weierstrass elliptic doubly periodic type solutions, and exponential solution. By employing the previously outlined method, they demonstrate their uniqueness for the given challenge. The results are presented in a clear and concise manner for various values of the necessary free parameters. Wolfram Mathematica's contour plot and 2D and 3D visualisations are used to show this process. The outcomes show how accurate, knowledgeable, and effective the computational procedures were. They may be used for increasingly complicated phenomena by integrating them with representational calculations. This finding constitutes a major advancement in our comprehension of the intricate and capricious behavior of this mathematical model.

    MSC: 35C07, 35C08, 35C09, 35G20
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    • Received Date: January 2025
    Accepted Date: April 2025
    Available online Date: May 2025
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