IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i11p2471-d1157440.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/11/2471/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/11/2471/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nikolay A. Kudryashov & Sofia F. Lavrova & Daniil R. Nifontov, 2023. "Bifurcations of Phase Portraits, Exact Solutions and Conservation Laws of the Generalized Gerdjikov–Ivanov Model," Mathematics, MDPI, vol. 11(23), pages 1-20, November.
    2. Peiyao Wang & Shangwen Peng & Yihao Cao & Rongpei Zhang, 2024. "The Conservative and Efficient Numerical Method of 2-D and 3-D Fractional Nonlinear Schrödinger Equation Using Fast Cosine Transform," Mathematics, MDPI, vol. 12(7), pages 1-14, April.
    3. Hamood Ur Rehman & Ifrah Iqbal & Suhad Subhi Aiadi & Nabil Mlaiki & Muhammad Shoaib Saleem, 2022. "Soliton Solutions of Klein–Fock–Gordon Equation Using Sardar Subequation Method," Mathematics, MDPI, vol. 10(18), pages 1-10, September.
    4. Zara, Aiman & Rehman, Shafiq Ur & Ahmad, Fayyaz & Kouser, Salima & Pervaiz, Anjum, 2022. "Numerical approximation of modified Kawahara equation using Kernel smoothing method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 169-184.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2471-:d:1157440. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.