1
Department of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, China.
2
Department of Mathematics, College of Science, University of Duhok , Duhok, Iraq.
10.22034/cmde.2025.65850.3052
Abstract
In this work, we investigate the dynamical behaviors of the well-known fractional generalized coupled nonlinear Schrodinger–Korteweg–de Vries equations, which have numerous applications in engineering and physics. These include the kinetics of short dispersive waves in narrow-bandwidth packets and the propagation of long waves in dispersive media. This model serves as a comprehensive framework for describing a wide range of physical phenomena, such as wave dynamics in optical fibers, communication systems, deep sea waves, plasmas, rogue waves, and atomic physics. We apply the complex wave transform with the M-fractional derivative to reduce the governing model to a nonlinear ordinary differential equation. To extract various optical soliton solutions, including mixed, dark, bright-dark, singular, kink-bright, complex, and combined solitons, we employ advanced analytical methods, namely the modified F-expansion method and the multivariate generalized exponential rational integral function technique. These methods enable the investigation of specific nonlinear phenomena and provide a more direct and simplified approximation of solutions compared to conventional techniques. To further illustrate the behavior of solutions under different parameter values, we include a variety of graphical representations. The effects of the fractional parameter are also examined. This study contributes significantly to the fields of nonlinear science and high-dimensional nonlinear wave theory by elucidating the nonlinear dynamic characteristics of the system and demonstrating the effectiveness of modern analytical approaches.
Muhammad, J. , Younas, U. and Murad, M. A. S. (2026). Exploring the fractional optical solitary wave structures with parametric effects to the generalized coupled nonlinear Schrodinger-KdV Equations. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.65850.3052
MLA
Muhammad, J. , , Younas, U. , and Murad, M. A. S. . "Exploring the fractional optical solitary wave structures with parametric effects to the generalized coupled nonlinear Schrodinger-KdV Equations", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2025.65850.3052
HARVARD
Muhammad, J., Younas, U., Murad, M. A. S. (2026). 'Exploring the fractional optical solitary wave structures with parametric effects to the generalized coupled nonlinear Schrodinger-KdV Equations', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.65850.3052
CHICAGO
J. Muhammad , U. Younas and M. A. S. Murad, "Exploring the fractional optical solitary wave structures with parametric effects to the generalized coupled nonlinear Schrodinger-KdV Equations," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2025.65850.3052
VANCOUVER
Muhammad, J., Younas, U., Murad, M. A. S. Exploring the fractional optical solitary wave structures with parametric effects to the generalized coupled nonlinear Schrodinger-KdV Equations. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2025.65850.3052
)