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Highly Dispersive Optical Soliton Perturbation, with Maximum Intensity, for the Complex Ginzburg–Landau Equation by Semi-Inverse Variation

Author

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  • Anjan Biswas

    (Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Hwy, 115409 Moscow, Russia
    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, Dunarea de Jos University of Galati, 111 Domneasca Street, 800201 Galati, Romania
    Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, South Africa)

  • Trevor Berkemeyer

    (Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762-4900, USA)

  • Salam Khan

    (Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762-4900, USA)

  • Luminita Moraru

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

  • Yakup Yıldırım

    (Department of Mathematics, Faculty of Arts and Sciences, Near East University, Nicosia 99138, Cyprus)

  • Hashim M. Alshehri

    (Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

This work analytically recovers the highly dispersive bright 1–soliton solution using for the perturbed complex Ginzburg–Landau equation, which is studied with three forms of nonlinear refractive index structures. They are Kerr law, parabolic law, and polynomial law. The perturbation terms appear with maximum allowable intensity, also known as full nonlinearity. The semi-inverse variational principle makes this retrieval possible. The amplitude–width relation is obtained by solving a cubic polynomial equation using Cardano’s approach. The parameter constraints for the existence of such solitons are also enumerated.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:987-:d:774778
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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. Zhang, Juan & Yu, Jian-Yong & Pan, Ning, 2005. "Variational principles for nonlinear fiber optics," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 309-311.
    3. Liu, W.Y. & Yu, Y.J. & Chen, L.D., 2007. "Variational principles for Ginzburg–Landau equation by He’s semi-inverse method," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1801-1803.
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