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A variety of solitons and other wave solutions of a nonlinear Schrödinger model relating to ultra-short pulses in optical fibers

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Abstract

This paper is performed to extract solitons and other solitary wave solutions of the generalized third-order nonlinear Schrödinger model by implementing two compatible schemes like improved auxiliary equation and enhanced rational \(({G}^{^{\prime}}/G)\)-expansion methods. The mentioned equation governs extensive applications in numerous disciplines of engineering and applied science and demonstrate how short-ultra pulses in optical fibers and quantum characteristics interact dynamically. A stack of hyperbolic, rational, and trigonometric function solitary wave solutions is magnificently constructed by means of the indicated schemes. Some of the acquired wave solutions are characterized graphically in 3D outlines, contour forms and 2D shapes to illustrate the dynamical behavior. The density of nonlinearity is brought out by contour plots and 2D outlines make clear the dynamic nature of pulse transmission. A comparable analysis of this study with the available consequences in literature confirms the innovation and assortment of present accomplished wave solutions and hence enhances the great performance of the employed techniques.

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Acknowledgements

The authors would like to acknowledge the financial support of the “Fundamental Research Grant Scheme (FRGS/1/2021/STG06/USM/02/09) by the Ministry of Higher Education, Malaysia, and Division of Research and Innovation, Universiti Sains Malaysia. The authors would also like to thank the School of Mathematical Sciences, University Sains Malaysia, Penang, Malaysia for the provided computing equipment.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Gelugor, Penang, Malaysia

    Md. Tarikul Islam & Farah Aini Abdullah

  2. Department of Mathematics, Hajee Mohammad Danesh Science and Technology University, Dinajpur, Bangladesh

    Md. Tarikul Islam

  3. CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca, Morelos, México

    J. F. Gómez-Aguilar

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  1. Md. Tarikul Islam
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  2. Farah Aini Abdullah
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  3. J. F. Gómez-Aguilar
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Contributions

MTI: Conceptualization, Methodology, Resources, Formal analysis, Writing-Original draft, Supervision; FAA: Conceptualization, Methodology, software, Writing-Original draft preparation; JFGA: Conceptualization, Methodology, Writing-review editing, Validation, Final draft preparation, Supervision.

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Correspondence to J. F. Gómez-Aguilar.

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Islam, M.T., Abdullah, F.A. & Gómez-Aguilar, J.F. A variety of solitons and other wave solutions of a nonlinear Schrödinger model relating to ultra-short pulses in optical fibers. Opt Quant Electron 54, 866 (2022). https://doi.org/10.1007/s11082-022-04249-8

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