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On the super solitonic structures for the fractional nonlinear Schrödinger equation

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Abstract

In this paper, the fractional nonlinear Schrödinger equation (NLSE) has been studied through conformable fraction space-time derivatives sense. Namely, we introduce some vital solutions for the fractional NLSE by using robust solver approach based on the Jacobian elliptic function method. This solver is easy to use, reliable, practical, and sturdy. The fractional properties structures that obtained from the equation are given in form of hyperbolic, soliton, shocks, explosive, superperiodic and trigonometric structures. It was noticed that raising the fractal factors causes the nonlinear wave to propagate with a different phase and wave frequency. The physical models describe the tidal energy generations play the important roles in the modern green power technologies. The solutions of nonlinear equations produce the parametric description for wave features in these processes. The solutions developed can be used in novel communications, energy applications, fractional quantum modes, and complicated astrophysical phenomena.

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Acknowledgements

The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number (IF2/PSAU/2022/01/23570).

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Authors and Affiliations

  1. Department of Chemistry, College of Science and Humanities, Prince Sattam Bin Abdulaziz University, 11942, Al-Kharj, Saudi Arabia

    Maged A. Azzam

  2. Department of Physics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, 11942, Al-Kharj, Saudi Arabia

    H. G. Abdelwahed

  3. Theoretical Physics Group, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    H. G. Abdelwahed & E. K. El-Shewy

  4. Department of Physics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

    E. K. El-Shewy

  5. Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

    Mahmoud A. E. Abdelrahman

  6. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Mahmoud A. E. Abdelrahman

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  1. Maged A. Azzam
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  2. H. G. Abdelwahed
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  3. E. K. El-Shewy
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  4. Mahmoud A. E. Abdelrahman
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Azzam, M.A., Abdelwahed, H.G., El-Shewy, E.K. et al. On the super solitonic structures for the fractional nonlinear Schrödinger equation. Opt Quant Electron 56, 750 (2024). https://doi.org/10.1007/s11082-023-06128-2

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