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Optical soliton solutions to the space–time fractional perturbed Schrödinger equation in communication engineering

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Abstract

The fractional perturbed nonlinear Schrödinger equation is important to model the dynamics of ultra-short pulses in lasers, solitons behavior in nonlinear optical fiber, signal processing, spectroscopy, etc. In this study, we construct assorted soliton solutions to the aforementioned equation utilizing a couple of analytical approaches, namely the \((G^{\prime}/G,1/G)\)-expansion method and the improved \(F\)-expansion method, to simulate the behavior of localized wave packets known as soliton in the presence of nonlinear perturbation and fractional derivatives through closed-form solutions. The solutions comprise arbitrary parameters, and for appropriate values of these parameters, several typical solitons, including compacton, periodic, irregular-periodic soliton, bell-shaped soliton, V-shaped soliton, kink, and some others are established. We investigate the effect of the fractional-order derivatives, and the graphs confirm that the fractional derivatives affect the amplitude, velocity, and width of the solitons. This study establishes the reliability of the implemented methods for finding soliton solutions of other nonlinear evolution equations.

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Acknowledgements

The authors would like to express their sincere thanks to the anonymous referees for their insightful remarks and recommendations to improve the article.

Funding

This work is supported by the Research Grant No.: A-124/5/52/RU/Science-46/2022-2023 and the authors acknowledge this support.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh

    M. Ali Akbar & Mst. Munny Khatun

Authors
  1. M. Ali Akbar
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  2. Mst. Munny Khatun
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Contributions

M. Ali Akbar: Conceptualization, Resources, Methodology, Project administration, Funding acquisition, Supervision, Writing-Original Draft. Mst. Munny Khatun: Data Curation, Formal Analysis, Software, Investigation, Validation, Visualization, Writing-Review Editing.

Corresponding author

Correspondence to M. Ali Akbar.

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Akbar, M.A., Khatun, M.M. Optical soliton solutions to the space–time fractional perturbed Schrödinger equation in communication engineering. Opt Quant Electron 55, 645 (2023). https://doi.org/10.1007/s11082-023-04911-9

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