IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3456-d922379.html
   My bibliography  Save this article

Optical Solitons with the Complex Ginzburg–Landau Equation with Kudryashov’s Law of Refractive Index

Author

Listed:
  • Ahmed H. Arnous

    (Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk Academy, Cairo 11837, Egypt)

  • Luminita Moraru

    (Department of Chemistry, Physics and Environment, Faculty of Sciences and Environment, Dunarea de Jos University of Galati, 47 Domneasca Street, 800008 Galati, Romania)

Abstract

In this paper, the optical solitons for the complex Ginzburg–Landau equation with Kudryashov’s law of refractive index are established. An improved modified extended tanh–function technique is used to extract numerous solutions. Bright and dark solitons, as well as singular soliton solutions, are achieved. In addition, as the modulus of ellipticity approaches unity or zero, solutions are formulated in terms of Jacobi’s elliptic functions, which provide solitons and periodic wave solutions.

Suggested Citation

  • Ahmed H. Arnous & Luminita Moraru, 2022. "Optical Solitons with the Complex Ginzburg–Landau Equation with Kudryashov’s Law of Refractive Index," Mathematics, MDPI, vol. 10(19), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3456-:d:922379
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3456/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/19/3456/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Elsayed M. E. Zayed & Khaled A. Gepreel & Mahmoud El-Horbaty & Anjan Biswas & Yakup Yıldırım & Hashim M. Alshehri, 2021. "Highly Dispersive Optical Solitons with Complex Ginzburg–Landau Equation Having Six Nonlinear Forms," Mathematics, MDPI, vol. 9(24), pages 1-19, December.
    2. Kudryashov, Nikolay A., 2020. "First integrals and general solution of the complex Ginzburg-Landau equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    3. Arnous, Ahmed H. & Biswas, Anjan & Yıldırım, Yakup & Zhou, Qin & Liu, Wenjun & Alshomrani, Ali S. & Alshehri, Hashim M., 2022. "Cubic–quartic optical soliton perturbation with complex Ginzburg–Landau equation by the enhanced Kudryashov’s method," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Han, Tianyong & Li, Zhao & Li, Chenyu, 2023. "Bifurcation analysis, stationary optical solitons and exact solutions for generalized nonlinear Schrödinger equation with nonlinear chromatic dispersion and quintuple power-law of refractive index in ," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).

    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, 2022. "Optical Solitons of the Generalized Nonlinear Schrödinger Equation with Kerr Nonlinearity and Dispersion of Unrestricted Order," Mathematics, MDPI, vol. 10(18), pages 1-9, September.
    2. Anjan Biswas & Jose Vega-Guzman & Yakup Yıldırım & Luminita Moraru & Catalina Iticescu & Abdulah A. Alghamdi, 2023. "Optical Solitons for the Concatenation Model with Differential Group Delay: Undetermined Coefficients," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    3. Arnous, Ahmed H. & Biswas, Anjan & Yıldırım, Yakup & Zhou, Qin & Liu, Wenjun & Alshomrani, Ali S. & Alshehri, Hashim M., 2022. "Cubic–quartic optical soliton perturbation with complex Ginzburg–Landau equation by the enhanced Kudryashov’s method," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Nikolay A. Kudryashov & Sofia F. Lavrova, 2023. "Painlevé Test, Phase Plane Analysis and Analytical Solutions of the Chavy–Waddy–Kolokolnikov Model for the Description of Bacterial Colonies," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    5. Xu, Guoan & Zhang, Yi & Li, Jibin, 2022. "Exact solitary wave and periodic-peakon solutions of the complex Ginzburg–Landau equation: Dynamical system approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 157-167.
    6. Zhu, Bo-Wei & Fang, Yin & Liu, Wei & Dai, Chao-Qing, 2022. "Predicting the dynamic process and model parameters of vector optical solitons under coupled higher-order effects via WL-tsPINN," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    7. Zayed, Elsayed M.E. & Alngar, Mohamed E.M. & Biswas, Anjan & Asma, Mir & Ekici, Mehmet & Alzahrani, Abdullah K. & Belic, Milivoj R., 2020. "Optical solitons and conservation laws with generalized Kudryashov’s law of refractive index," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    8. Han, Tianyong & Li, Zhao & Li, Chenyu, 2023. "Bifurcation analysis, stationary optical solitons and exact solutions for generalized nonlinear Schrödinger equation with nonlinear chromatic dispersion and quintuple power-law of refractive index in ," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    9. Anjan Biswas & Trevor Berkemeyer & Salam Khan & Luminita Moraru & Yakup Yıldırım & Hashim M. Alshehri, 2022. "Highly Dispersive Optical Soliton Perturbation, with Maximum Intensity, for the Complex Ginzburg–Landau Equation by Semi-Inverse Variation," Mathematics, MDPI, vol. 10(6), pages 1-11, March.
    10. Kudryashov, Nikolay A., 2020. "Optical solitons of model with integrable equation for wave packet envelope," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

    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:10:y:2022:i:19:p:3456-:d:922379. 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.