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Optical soliton and other solutions to the nonlinear dynamical system via two efficient analytical mathematical schemes

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Abstract

This article will discuss the (2+1)-dimensional nonlinear dynamical conformable generalized Schrödinger system to represent the optical pulse propagation in monomode optical fibers. Optical soliton solutions of the given equations will be found using novel tools, namely the new extended hyperbolic function method and the Sine-Gordon equation expansion method. The suggested methods will extract various solutions such as optical bright, dark, singular, periodic, combined bright-drak, and mixed singular soliton solutions. The derived solutions are explained using contour graphs, 3-dimensional surface graphs, and 2-dimensional line profiles to visualize the theoretical outcomes. The dynamics of exact explicit solutions of nonlinear dynamical systems play a crucial role in the theory of solitons and the formations of exact analytical solutions perform an important role in the area of nonlinear sciences and applied mathematics. Moreover, these analytical solutions may ensure dynamical and physical behavior of the system which assist us about the mechanism of considered complex nonlinear systems. This work allows the reader to get a better understanding of the various techniques that have been disputed. The obtained findings reveal that the procedures we have adopted are straightforward, powerful, effective, and precise to implement and that they apply to a wide range of more challenging issues.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 52071298), the Strategic Research and Consulting Project of Chinese Academy of Engineering (No. 2022HENYB05), the ZhongYuan Science and Technology Innovation Leadership Program (No. 214200510010). The authors would like to extend their sincere appreciation to Researchers Supporting Project number (RSPD2023R802) King Saud University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Henan Academy of Big Data/School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

    Muhammad Bilal & Jingli Ren

  2. Department of Medical Research, China Medical University, Taichung, 40402, Taiwan

    Mustafa Inc

  3. Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia

    Reem K. Alhefthi

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  1. Muhammad Bilal
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  2. Jingli Ren
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  4. Reem K. Alhefthi
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All authors contributed to the study conception and design. All authors read and approved the final manuscript.

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Bilal, M., Ren, J., Inc, M. et al. Optical soliton and other solutions to the nonlinear dynamical system via two efficient analytical mathematical schemes. Opt Quant Electron 55, 938 (2023). https://doi.org/10.1007/s11082-023-05103-1

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