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New solitary wave solutions to Biswas–Milovic and resonant nonlinear Schrödinger equations

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Abstract

This paper explore the new solitary wave solutions of the Biswas–Milovic equation and resonant nonlinear Schr\(\ddot{o}\)dinger equations with Kerr–Law nonlinearity. In mathematical physics, the Biswas–Milovic equation plays an important role. The dynamics of these solitons are well known to propagate over large distances in a few femto-seconds through these fibres. These dynamics are governed by the nonlinear Schrödinger’s equation. The resonant nonlinear Schrödinger equation can be used to model the propagation of waves in fiber optics. The powerful analytical approach known as the extended simple equation method is employed to explore the solitary wave solutions of the Biswas–Milovic and resonant nonlinear Schr\(\ddot{o}\)dinger equations. These equations are primarily explored in the realm of solitons in nonlinear fiber optics. New dark, kink, anti-kink and singular periodic solitons are secured. Furthermore, 3D surface graphs, contour plots and parametric graphs are drawn to show dynamical behavior of some obtained solutions with the aid of symbolic software such as Mathematica. The constructed solutions will helpful to understand the dynamical framework of nonlinear Schr\(\ddot{o}\)dinger equations in the related physical phenomena.

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Data will be provided on request to the corresponding author.

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Acknowledgements

The Authors extend their appreciation to the Deanship Scientific Research at King Khalid University for funding this work through large group Research Project under grant number: RGP2/422/44.

Funding

This research work was supported by the Deanship of Scientific Research at King Khalid University under grant number: RGP2/422/44.

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Authors and Affiliations

  1. Division of Science and Technology, Department of Mathematics, University of Education, Lahore, Pakistan

    Wardat us Salam & Robina Rafeeq

  2. Department of Mathematics, GC Women University, Sialkot, Pakistan

    Hira Tariq

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

    Hijaz Ahmad

  4. Civil Engineering Department, College of Engineering, King Khalid University, Abha, Saudi Arabia

    Khaled Mohamed Khedher

  5. Department of Mathematics and Informatics, Azerbaijan University, Jeyhun Hajibeyli street, 71, AZ1007, Baku, Azerbaijan

    Hijaz Ahmad

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

    Hijaz Ahmad

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

    Hijaz Ahmad

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  1. Wardat us Salam
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  2. Hira Tariq
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  3. Robina Rafeeq
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  4. Hijaz Ahmad
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  5. Khaled Mohamed Khedher
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Contributions

Conceptualization: WS, data curation: RR, formal analysis: HT, validation: HT, writing—original draft: WS, writing—review editing: HA.

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Correspondence to Hijaz Ahmad.

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us Salam, W., Tariq, H., Rafeeq, R. et al. New solitary wave solutions to Biswas–Milovic and resonant nonlinear Schrödinger equations. Opt Quant Electron 56, 744 (2024). https://doi.org/10.1007/s11082-024-06286-x

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