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Solitons and modulation instability of the perturbed Gerdjikov–Ivanov equation with spatio-temporal dispersion

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  • Al-Kalbani, Kaltham K.
  • Al-Ghafri, K.S.
  • Krishnan, E.V.
  • Biswas, Anjan

Abstract

This paper is exploring the optical solitons to perturbed Gerdjikov–Ivanov (GI) equation in optical fibers. Using traveling wave transformation, the complex form of perturbed GI equation is reduced to a nonlinear ordinary differential equation (ODE). Then, the improved projective Riccati equations method has been implemented to solve the ODE analytically. Different types of solutions such as bright, kink and singular optical soliton structures are obtained. In addition, W-shaped, kink-dark and singular-kink waves are obtained under specific values for the physical parameters in the model. The existence conditions of all optical solitons are given. Also, the behaviors of some optical solitons are illustrated graphically in this paper by selecting appropriate values for the physical parameters. Besides, the modulation instability of the perturbed GI equation is reported.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008778
    DOI: 10.1016/j.chaos.2021.111523
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    References listed on IDEAS

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    1. Zeng, Liangwei & Mihalache, Dumitru & Malomed, Boris A. & Lu, Xiaowei & Cai, Yi & Zhu, Qifan & Li, Jingzhen, 2021. "Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Susanto, Hadi & Malomed, Boris A., 2021. "Embedded solitons in second-harmonic-generating lattices," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
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    1. 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.
    2. 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.

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