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General solitons for eighth-order dispersive nonlinear Schrödinger equation with ninth-power law nonlinearity using improved modified extended tanh method

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Abstract

Higher-order nonlinear Schrödinger equation is necessarily needed to suit with the light propagation in optical fibers, wherein the effect of higher-order nonlinear and dispersive effects should be taken into account. Due to the increase of these physical effects, the theoretical analysis and experimental observation of optical solitons are more difficult, but the generated optical solitons will bring more novel nonlinear phenomena and reveal more fundamental nonlinear mechanisms. In this paper, we study the eighth order non-linear Schrödinger equation (NLSE) with ninth power law of nonlinearity. Studying is conducted by applying the improved modified extended tanh method to secure various optical soliton solutions. These solutions are important in applied physics and engineering. The obtained results can be used to understand and elucidate the physical nature of waves spread in a dispersive medium. The extracted solutions including dark, bright and singular solitons. In addition, we extract periodic solutions, singular periodic solutions and Weierstrass elliptic solutions for the proposed model. Furthermore, graphical simulations for some solutions are depicted to demonstrate the powerful of these solutions. This influential, consistent, and effective method can be used to solve a variety of other models in physics and other applied sciences.

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia, for funding this work through the Re-search Group Project under Grant No. (RGP.1/244/44).

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Authors and Affiliations

  1. Department of Physics and Mathematics Engineering, Faculty of Engineering, Ain Shams University, Cairo, Egypt

    Islam Samir

  2. Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia

    Assmaa Abd-Elmonem

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

    Hamdy M. Ahmed

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  1. Islam Samir
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  2. Assmaa Abd-Elmonem
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  3. Hamdy M. Ahmed
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IS Methodology, Validation, Software. AAE Writing- Reviewing and Editing, HMA Validation, Writing- Reviewing and Editing, Investigation, Supervision.

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Correspondence to Hamdy M. Ahmed.

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Samir, I., Abd-Elmonem, A. & Ahmed, H.M. General solitons for eighth-order dispersive nonlinear Schrödinger equation with ninth-power law nonlinearity using improved modified extended tanh method. Opt Quant Electron 55, 470 (2023). https://doi.org/10.1007/s11082-023-04753-5

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