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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
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    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).
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    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).

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