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Exploring of soliton solutions in optical metamaterials with parabolic law of nonlinearity

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Abstract

In this article, we examine the nonlinear Schrödinger equation governing the dynamics of electromagnetic pulse in metamaterials revealing a parabolic law of nonlinearity. The Sub-sardar equation method is used to examine and comprehend the solutions to the nonlinear Schrödinger equation better. This method allows one to derive dark, bright, singular-bright, and periodic solitons, among other types of soliton solutions. The complex dynamics of electromagnetic pulses in metamaterials are largely dependent on soliton dynamics, which are stable, localized wave packets that preserve their amplitude and shape during propagation. Metamaterials are engineered materials with unique electromagnetic properties not found in nature, and studying the dynamics of electromagnetic pulses within them is essential for advancing applications in fields such as optics and telecommunications. Additionally, the study conducts stability and sensitivity analyses for the obtained results, going beyond theoretical derivations. To facilitate the visual understanding of the solutions the 3D, 2D and contour graphs of achieved solutions are also presented.

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Acknowledgements

This work is supported by Research Supporting Project Number (RSPD2024R1007), King Saud University, Riyadh, Saudi Arabia. National Natural Science Foundation of China (NSFC) under Grant No. 72293574, the Natural Science Foundation of Hunan Province under Grant No. 2022JJ30677, and the National Key Research and Development Program of China under Grant No. 2022YFC3303303.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    Muhammad Shakeel & Xinge Liu

  2. Department of Information Systems, College Computers and Information Science, King Saud University, Riyadh, Saudi Arabia

    Almetwally M. Mostafa

  3. Computer Engineering Department, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia

    Salman A. AlQahtani

  4. Islamic Studies Department, College of Education, King Saud University, Riyadh, Saudi Arabia

    Nouf F. AlQahtani

  5. Basic Engineering Science Department, Benha Faculty of Engineering, Benha University, Benha, Egypt

    Mohamed R. Ali

  6. Faculty of Engineering and Technology, Future University in Egypt, New Cairo, 11835, Egypt

    Mohamed R. Ali

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  1. Muhammad Shakeel
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  3. Almetwally M. Mostafa
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Shakeel, M., Liu, X., Mostafa, A.M. et al. Exploring of soliton solutions in optical metamaterials with parabolic law of nonlinearity. Opt Quant Electron 56, 860 (2024). https://doi.org/10.1007/s11082-024-06452-1

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