Modeling and Exploration of Localized Wave Phenomena in Optical Fibers Using the Generalized Kundu–Eckhaus Equation for Femtosecond Pulse Transmission
Ejaz Hussain, Ali H. Tedjani, Khizar Farooq, Beenish
Abstract
This manuscript aims to explore localized waves for the nonlinear partial differential equation referred to as the (1+1)-dimensional generalized Kundu–Eckhaus equation with an additional dispersion term that describes the propagation of the ultra-short femtosecond pulses in an optical fiber. This research delves deep into the characteristics, behaviors, and localized waves of the (1+1)-dimensional generalized Kundu–Eckhaus equation. We utilize the multivariate generalized exponential rational integral function method (MGERIFM) to derive localized waves, examining their properties, including propagation behaviors and interactions. Motivated by the generalized exponential rational integral function method, it proves to be a powerful tool for finding solutions involving the exponential, trigonometric, and hyperbolic functions. The solutions we found using the MGERIF method have important applications in different scientific domains, including nonlinear optics, plasma physics, fluid dynamics, mathematical physics, and condensed matter physics. We apply the three-dimensional (3D) and contour plots to illuminate the physical significance of the derived solution, exploring the various parameter choices. The proposed approaches are significant and applicable to various nonlinear evolutionary equations used to model nonlinear physical systems in the field of nonlinear sciences.