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<p>In this study, a fractional coupled nonlinear Schrödinger model is investigated. The model characterizes the amplitude of circularly polarized waves in nonlinear fiber optics. Using the fractional wave transformation and conformable fractional derivatives, analytical soliton solutions are obtained. All the exact wave solutions are in the form of Jaccobi elliptic, trigonometric, hyperbolic, and rational functions, and they are obtained using symbolic computations. The results are derived using a new analytical technique, namely, the Kumar–Malik method. By means of this approach, we obtained different types of solutions, including bright solitons, dark solitons, and different solitary wave solutions. To elucidate the physical behavior of these solutions, the analytical results are presented in the form of two- and three-dimensional graphs. The analytical technique used in this work may be employed to analyze advanced fractional-order models in fields, such as optics, hydrodynamics, plasma, and wave theory.</p>

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Nonlinear traveling-wave solutions of a fractional Schrödinger system through a Kumar–Malik-like approach

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Nauman Ahmed,
  • Jorge E. Macías-Díaz,
  • Makhdoom Ali,
  • Naveed Shahid,
  • Muhammad Z. Baber,
  • Siegfried Macías

摘要

In this study, a fractional coupled nonlinear Schrödinger model is investigated. The model characterizes the amplitude of circularly polarized waves in nonlinear fiber optics. Using the fractional wave transformation and conformable fractional derivatives, analytical soliton solutions are obtained. All the exact wave solutions are in the form of Jaccobi elliptic, trigonometric, hyperbolic, and rational functions, and they are obtained using symbolic computations. The results are derived using a new analytical technique, namely, the Kumar–Malik method. By means of this approach, we obtained different types of solutions, including bright solitons, dark solitons, and different solitary wave solutions. To elucidate the physical behavior of these solutions, the analytical results are presented in the form of two- and three-dimensional graphs. The analytical technique used in this work may be employed to analyze advanced fractional-order models in fields, such as optics, hydrodynamics, plasma, and wave theory.