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Optical soliton solutions to transmission of monochromatic optical radiation of the paraxial wave dynamical model with Kerr media

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Abstract

In this article, the modified extended Fan sub-equation approach as an analytical tool to investigate the optical soliton solutions of the paraxial wave dynamical model with Kerr media. Indistinguishable and non-diffractive spatially scattered waves transmitting in the optical Kerr medium are explained by optical solitary waves. The solitons, single and mixed non-degenerate Jacobi elliptic function type solutions of the time-dependent dimensionless paraxial wave equation are assembled using the modified extended Fan sub-equation approach. The aforementioned approach offers new, comprehensive solutions that are relatively easy to implement, in contrast to earlier continuous strategies. This technique uses a traveling wave transformation to convert a non-linear partial differential equation into an ODE. The developed wave solutions have substantial significance in the fields of science and engineering. Visual illustrations of various soliton layouts can be achieved by supplying suitable values for the parameters via this technique. The computer software Mathematica 13.2 is used to illustrate several modulus, real, and imaginary solutions visually in the form of contour, 2D, and 3D visualizations that help understand the concrete importance of the paraxial wave dynamical model. The results are fascinating and can potentially be helpful in investigating the stochastic aspects of many nonlinear physical theories that arise in optical studies and a number of other scientific fields.

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Acknowledgements

The authors would like to acknowledge Deanship of Graduate Studies and Scientific Research, Taif University for funding this work. The authors are also grateful to anonymous referees for their valuable suggestions, which significantly improved this manuscript.

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The author(s) received no external funding for this study.

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Authors and Affiliations

  1. Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan

    Muhammad Zain Yousaf, Muhammad Abbas & Tahir Nazir

  2. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia

    Farah Aini Abdullah

  3. Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, 21944, Taif, Saudi Arabia

    Moataz Alosaimi

Authors
  1. Muhammad Zain Yousaf
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  2. Muhammad Abbas
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  3. Tahir Nazir
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  4. Farah Aini Abdullah
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  5. Moataz Alosaimi
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Contributions

MZY: Methodology, Writing–original draft. MA: Supervision, Methodology, Writing–review and editing. TN: Supervision, Methodology, Writing–review and editing. FAA: Visualization, Formal Analysis, Validation. M.Alosaimi: Investigation, Visualization, Software, Validation, Writing–review and editing. All authors have read and agreed to publish the manuscript.

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Correspondence to Muhammad Zain Yousaf.

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Yousaf, M.Z., Abbas, M., Nazir, T. et al. Optical soliton solutions to transmission of monochromatic optical radiation of the paraxial wave dynamical model with Kerr media. Opt Quant Electron 56, 1123 (2024). https://doi.org/10.1007/s11082-024-06993-5

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