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Soliton solutions of optical pulse envelope \(E(Z,\tau)\) with \(\nu\)-time derivative

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Abstract

The nonlinear Schrödinger equation (NLSE), which governs the propagation of pulses in optical fiber while including the effects of second, third, and fourth-order dispersion, is crucial for a comprehensive understanding of pulse propagation in optical communication systems. It assists engineers and scientists in optimizing and controlling the behavior of ultra-short pulses in complex and real-world optical systems. In this study, we solve the generalized NLSE for the pulse envelope \({E}(z, \tau )\) with \(\nu\)-time derivative by employing the Sardar subequation method (SSM). We obtain new soliton solutions corresponding to the relevant parameters of this technique. Additionally, conditions depending on the parameters of optical pulse envelope \({E}(z,\tau )\) are provided for the existence of such soliton structures. Furthermore, the solitary wave solutions are expressed in the form of generalized trigonometric and hyperbolic functions. The dynamic behaviours of the solutions are revealed with specific values of the parameters that satisfy their respective existence criteria. The results indicate that SSM demonstrates high reliability, simplicity, and adaptability for use with various nonlinear equations.

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Funding

The research is supported by: Guangdong basic applied basic research foundation (2021A1515110566), Guangdong philosophy and social science planning project (GD22YGL03), 2021 annual project of Guangzhou philosophy and social science planning (2021GZGJ50).

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Authors and Affiliations

  1. International Business School, Guangdong University of Finance & Economics, Foshan, 528100, China

    Renfei Luo

  2. Department of Mathematics, Forman Christian College University, Lahore, Pakistan

    Khalida Faisal

  3. Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran

    Hadi Rezazadeh

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

    Hijaz Ahmad

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

    Hijaz Ahmad

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

    Hijaz Ahmad

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

    Hijaz Ahmad

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  1. Renfei Luo
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  2. Khalida Faisal
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Conceptualization: RL; Data curation: KF; Formal analysis: HR; Validation: KF; Writing-original draft: HR; Writing–review editing: HA.

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Correspondence to Hijaz Ahmad.

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Luo, R., Faisal, K., Rezazadeh, H. et al. Soliton solutions of optical pulse envelope \(E(Z,\tau)\) with \(\nu\)-time derivative. Opt Quant Electron 56, 719 (2024). https://doi.org/10.1007/s11082-023-06146-0

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