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Abundant M-fractional optical solitons to the pertubed Gerdjikov–Ivanov equation treating the mathematical nonlinear optics

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Abstract

In this paper, the perturbed Gerdjikov–Ivanov (GI) equation using a truncated M-fractional derivative is studied in mathematical nonlinear optics. We are explored its novel dark and other soliton solutions and compared them with the existing results. To obtain the objective, two particular methods, the modified extended \(\tanh\) expansion method and the \(Exp_a\) function method, are implemented. In this exercise, an arrangement of exact solitons is received as well as verified by utilizing the symbolic soft computations. The dynamical characteristics of the obtained results, along with a fractional parameter, are also discussed via two and three-dimensional graphs. These solutions are suggested that the employed methods are impressive, determined and smooth as compared to many other methods. The work of this paper is of high importance regarding its applications in photonic crystal fibers and mathematical physics.

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Authors and Affiliations

  1. Department of Mathematics, COMSATS University, Vehari Campus, Islamabad, Pakistan

    Asim Zafar & Muhammad Raheel

  2. Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt

    Khalid K. Ali

  3. Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser 11991, Prince Sattam bin Abdulaziz University, Al-Kharj, Saudi Arabia

    Kottakkaran Sooppy Nisar

  4. Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, 26030, Eskisehir, Turkey

    Ahmet Bekir

Authors
  1. Asim Zafar
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  2. Khalid K. Ali
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  3. Muhammad Raheel
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  4. Kottakkaran Sooppy Nisar
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  5. Ahmet Bekir
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Correspondence to Asim Zafar or Ahmet Bekir.

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Zafar, A., Ali, K.K., Raheel, M. et al. Abundant M-fractional optical solitons to the pertubed Gerdjikov–Ivanov equation treating the mathematical nonlinear optics. Opt Quant Electron 54, 25 (2022). https://doi.org/10.1007/s11082-021-03394-w

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