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Traveling Wave Optical Solutions for the Generalized Fractional Kundu–Mukherjee–Naskar (gFKMN) Model

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  • Yong Tang

    (College of Computer Science, Chengdu University, Chengdu 610106, China)

Abstract

The work considers traveling wave optical solutions for the nonlinear generalized fractional KMN equation. This equation is considered for describing pulse propagation in optical fibers and communication systems using two quite similar approaches, based on the expansion of these solutions in the exponential or polynomial forms. Both approaches belong to the direct solving class of methods for PDEs and suppose the use of an auxiliary equation. The solutions acquired in this paper are obtained from first- and second-order differential equations that act as auxiliary equations. In addition, we generated 3D, contour, and 2D plots to illustrate the characteristics of the obtained soliton solutions. To create these plots, we carefully selected appropriate values for the relevant parameters.

Suggested Citation

  • Yong Tang, 2023. "Traveling Wave Optical Solutions for the Generalized Fractional Kundu–Mukherjee–Naskar (gFKMN) Model," Mathematics, MDPI, vol. 11(11), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2583-:d:1164211
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    References listed on IDEAS

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    1. M. Abu-Shady & Mohammed K. A. Kaabar, 2021. "A Generalized Definition of the Fractional Derivative with Applications," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-9, October.
    2. Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    3. Muhammad Naeem & Hadi Rezazadeh & Ahmed A. Khammash & Rasool Shah & Shamsullah Zaland & Melike Kaplan, 2022. "Analysis of the Fuzzy Fractional-Order Solitary Wave Solutions for the KdV Equation in the Sense of Caputo-Fabrizio Derivative," Journal of Mathematics, Hindawi, vol. 2022, pages 1-12, March.
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