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Optical Solitons and Modulation Instability Analysis with Lakshmanan–Porsezian–Daniel Model Having Parabolic Law of Self-Phase Modulation

Author

Listed:
  • Kaltham K. Al-Kalbani

    (Department of Mathematics, Sultan Qaboos University, P.O. Box 36, Al-Khod, Muscat 123, Oman)

  • Khalil S. Al-Ghafri

    (College of Applied Sciences, University of Technology and Applied Sciences, P.O. Box 14, Ibri 516, Oman)

  • Edamana V. Krishnan

    (Department of Mathematics, Sultan Qaboos University, P.O. Box 36, Al-Khod, Muscat 123, Oman)

  • Anjan Biswas

    (Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245, USA
    Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, 800201 Galati, Romania
    Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, Pretoria 0204, South Africa)

Abstract

This paper seeks to find optical soliton solutions for Lakshmanan–Porsezian–Daniel (LPD) model with the parabolic law of nonlinearity. The spatiotemporal dispersion is included to the model, as it can contribute to handling the problem of internet bottleneck. This study was performed analytically using the traveling wave hypothesis to reduce the model to an integrable form. Then, the resulting equation was handled with two approaches, namely, the auxiliary equation method and the Bernoulli subordinary differential equation (sub-ODE) method. With an intentional focus on hyperbolic function solutions, abundant optical soliton waves including W-shaped, bright, dark, kink-dark, singular, kink, and antikink solitons were derived with the existing conditions. Furthermore, the behaviors of some optical solitons are illustrated. The spatiotemporal dispersion was found to significantly affect the pulse propagation dynamics. Finally, the modulation instability (MI) of the LPD model is explained in detail along with the extraction of the expression of MI gain.

Suggested Citation

  • Kaltham K. Al-Kalbani & Khalil S. Al-Ghafri & Edamana V. Krishnan & Anjan Biswas, 2023. "Optical Solitons and Modulation Instability Analysis with Lakshmanan–Porsezian–Daniel Model Having Parabolic Law of Self-Phase Modulation," Mathematics, MDPI, vol. 11(11), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2471-:d:1157440
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    References listed on IDEAS

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    1. Nur Hasan Mahmud Shahen & Foyjonnesa & Md Habibul Bashar & Tasnim Tahseen & Sakhawat Hossain, 2021. "Solitary and Rogue Wave Solutions to the Conformable Time Fractional Modified Kawahara Equation in Mathematical Physics," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-9, July.
    2. Al-Kalbani, Kaltham K. & Al-Ghafri, K.S. & Krishnan, E.V. & Biswas, Anjan, 2021. "Solitons and modulation instability of the perturbed Gerdjikov–Ivanov equation with spatio-temporal dispersion," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
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