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Soliton solutions, stability, and modulation instability of the (2+1)-dimensional nonlinear hyperbolic Schrödinger model

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Abstract

In this article, the (2+1)-dimensional nonlinear hyperbolic Schrödinger model is studied analytically which specifies the proliferation of optics signal in single-mode fiber optics by using the unified technique, the exp(-\(\delta (\zeta )\)) technique and the polynomial expansion technique. These techniques can give solutions of different kind that has application in physical mathematical fields, optical wave structure, and many other fields that are related to wave transmission. As compared to other approaches these used methodology are effective, unique, and easy to applicable for solving the complex models in Physics. The waveform in electromagnetic domains topics are discussed using this model as a governing equation. For a given set of pertinent parameters, the dynamics of various wave structures are visualised in 3D, 2D, and contour using Mathematica. These solutions exhibit singular periodic, multi-periodic, optical, singular and multiple bell-shaped, and μ-shaped solitons solutions as their behaviour. Further we study the stability and modulation instability (MI), also some plots are drawn for better understanding of solution. The solutions derived from the utilized techniques describe that these approches are easy, potent and uncomplicated, and these can be applicable for solving many other NLSE in Mathematical physics, and also in different field of natural sciences. The solution obtain are newly made because according to my best knowledge these methodology are not applied to this model in previous.

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Acknowledgements

The researchers wish to extend their sincere gratitude to the Deanship of Scientific Research at the Islamic University of Madinah for the support provided to the Post-Publishing Program.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, Saudi Arabia

    M. Adel & Hijaz Ahmad

  2. Department of Mathematics, Mirpur University of Science and Technology, Mirpur, 10250, AJK, Pakistan

    Kalim U. Tariq & S. M. Raza Kazmi

  3. Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey

    Hijaz Ahmad

  4. Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, Mishref, Kuwait

    Hijaz Ahmad

  5. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

    Hijaz Ahmad

Authors
  1. M. Adel
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  2. Kalim U. Tariq
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  3. Hijaz Ahmad
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  4. S. M. Raza Kazmi
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Contributions

M. Adel: Methodology, project administration. Kalim U. Tariq:conceptualization, supervision. Hijaz Ahmad: Identification of the research problem, validation, review and editing. S. M. Raza Kazmi: Formal analysis and investigation, writing original draft, visualization.

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Correspondence to Hijaz Ahmad.

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Adel, M., Tariq, K.U., Ahmad, H. et al. Soliton solutions, stability, and modulation instability of the (2+1)-dimensional nonlinear hyperbolic Schrödinger model. Opt Quant Electron 56, 182 (2024). https://doi.org/10.1007/s11082-023-05570-6

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