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Dynamical behavior of the fractional generalized nonlinear Schrödinger equation of third-order

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Abstract

The generalized nonlinear Schrödinger equation with M-truncated derivatives (GNLSE-MTD) is studied here. By using generalized Riccati equation and mapping methods, new elliptic, hyperbolic, trigonometric, and rational solutions are discovered. Because the GNLSE is widely employed in communication, heat pulse propagation in materials, optical fiber communication systems, and nonlinear optical phenomena, the resulting solutions may be used to analyze a wide variety of important physical phenomena. The dynamic behaviors of the various derived solutions are interpreted using 3-D and 2-D graphs to explain the affects of M-truncated derivatives. We can deduce that the surface shifts to the left when the order of M-truncated derivatives decreases.

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Acknowledgements

This research has been funded by the Scientific Research Deanship at the University of Ha’il-Saudi Arabia through project number RG-23237.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, University of Ha’il, 2440, Ha’il, Saudi Arabia

    Athar I. Ahmed, Mohamed S. Algolam, F. Gassem & Wael W. Mohammed

  2. Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186, Roma, Italy

    Clemente Cesarano

  3. Department of Mathematics, College of Science and Arts in Al-Asyah, Qassim University, 6640, Buraidah, Saudi Arabia

    Doaa Rizk

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

    Wael W. Mohammed

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  1. Athar I. Ahmed
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Correspondence to Wael W. Mohammed.

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Ahmed, A.I., Algolam, M.S., Cesarano, C. et al. Dynamical behavior of the fractional generalized nonlinear Schrödinger equation of third-order. Opt Quant Electron 56, 843 (2024). https://doi.org/10.1007/s11082-024-06626-x

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