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Soliton solutions and fractional-order effect on solitons to the nonlinear optics model

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Abstract

The space–time fractional nonlinear Tzitzeica–Dodd–Bullough (TDB) equation is an important model in nonlinear optics, quantum field theory, plasma physics, solid-state physics among other domains. Through the Painlevé and fractional wave transformations, the space–time fractional nonlinear TDB equation has been converted to a nonlinear equation. Broad-spectral and standard closed-form soliton solutions in the form of exponential, rational, trigonometric, and hyperbolic functions with free parameters have been achieved using the improved Bernoulli sub-equation function (IBSEF) approach. The solutions established in this article are comprehensive and sophisticated, and the results found in the literature are a special case of the results obtained. The effect of the fractional parameter \(\mu\) on the wave profiles of the phenomena has been examined by defining 3D, 2D, and contour plots of the soliton solutions, and it is found that the fractional parameter has a significant impact. The results attained demonstrate that the IBSEF approach is compatible, useful, and capable of providing wide-spectral analytical wave solutions to fractional nonlinear models arising in optics, mathematical physics, and engineering.

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Acknowledgements

The authors are grateful to the anonymous referees for their insightful comments and suggestions to improve the article.

Funding

This work is done under financial support from the Ministry of Higher Education Malaysia (MoHE) for the Fundamental Research Grant Scheme, Acct No: FRGS/1/2021/STG06/USM/02/9 and the authors gratefully acknowledge this support.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia

    M. Ali Akbar & Farah Aini Abdullah

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

    M. Ali Akbar & Md. Morshedul Haque

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  1. M. Ali Akbar
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  2. Farah Aini Abdullah
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  3. Md. Morshedul Haque
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MAA: Conceptualization, Formal analysis, Writing-original draft, Investigation, Resources, Validation, Data curation. FAA: Supervision, Project administration, Funding acquisition. MMH: Visualization, Writing-review editing, Software, Methodology.

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Correspondence to M. Ali Akbar.

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Akbar, M., Abdullah, F.A. & Haque, M. Soliton solutions and fractional-order effect on solitons to the nonlinear optics model. Opt Quant Electron 54, 461 (2022). https://doi.org/10.1007/s11082-022-03839-w

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