Optical soliton solution for dual-mode time-fractional nonlinear Schrödinger equation by generalized exponential rational function method
Muhammad Amin S. Murad, Salim S. Mahmood, Homan Emadifar, Wael W. Mohammed, Karim K. Ahmed
Abstract
In this paper, the generalized exponential rational function method (GERFM) is applied to study the dual-mode nonlinear Schrödinger equation (DMNLSE) and construct various novel soliton solutions. Several new optical solutions, including wave, dark, bright, mixed dark-bright, and singular solitons, are successfully derived. These solutions are visualized through contour plots, as well as two-dimensional and three-dimensional graphical simulations. Furthermore, the influence of the conformable derivative parameter and temporal parameter on the optical solitons is analyzed, emphasizing their crucial roles in shaping soliton properties. Contour plots illustrate the structural stability of the solitons for different fractional orders, while temporal evolution graphs confirm their robustness over time. A key contribution of this study is its exploration of fractional order dynamics and their impact on soliton behavior, enabling optimizing of soliton characteristics. This research advances the theoretical framework of DMNLSE and paves the way for practical applications in modeling wave propagation in nonlinear optical fibers , quantum systems, and fluid mechanics. By integrating a robust analytical approach with comprehensive graphical analyses, this work establishes a foundation for future research in nonlinear dynamics and soliton theory.