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Analytical Solutions of the Fractional Complex Ginzburg‐Landau Model Using Generalized Exponential Rational Function Method with Two Different Nonlinearities

Author

Listed:
  • Ghazala Akram
  • Maasoomah Sadaf
  • M. Atta Ullah Khan
  • Hasan Hosseinzadeh

Abstract

The complex Ginzburg‐Landau model appears in the mathematical description of wave propagation in nonlinear optics. In this paper, the fractional complex Ginzburg‐Landau model is investigated using the generalized exponential rational function method. The Kerr law and parabolic law are considered to discuss the nonlinearity of the proposed model. The fractional effects are also included using a novel local fractional derivative of order α. Many novel solutions containing trigonometric functions, hyperbolic functions, and exponential functions are acquired using the generalized exponential rational function method. The 3D‐surface graphs, 2D‐contour graphs, density graphs, and 2D‐line graphs of some retrieved solutions are plotted using Maple software. A variety of exact traveling wave solutions are reported including dark, bright, and kink soliton solutions. The nature of the optical solitons is demonstrated through the graphical representations of the acquired solutions for variation in the fractional order of derivative. It is hoped that the acquired solutions will aid in understanding the dynamics of the various physical phenomena and dynamical processes governed by the considered model.

Suggested Citation

  • Ghazala Akram & Maasoomah Sadaf & M. Atta Ullah Khan & Hasan Hosseinzadeh, 2023. "Analytical Solutions of the Fractional Complex Ginzburg‐Landau Model Using Generalized Exponential Rational Function Method with Two Different Nonlinearities," Advances in Mathematical Physics, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlamp:v:2023:y:2023:i:1:n:9720612
    DOI: 10.1155/2023/9720612
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    References listed on IDEAS

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    1. Shao-Wen Yao & Esin Ilhan & P. Veeresha & Haci Mehmet Baskonus, 2021. "A Powerful Iterative Approach For Quintic Complex Ginzburg–Landau Equation Within The Frame Of Fractional Operator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-13, August.
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