Theoretical Insights into Pulse Dynamics in Nonlinear Optical Media

Abstract

The study of nonlinear partial differential equations (NLPDEs) is one of the most excit ing areas of practical mathematics. Some real-life events can be described, modeled, and predicted using these equations. However, determining their precise answers is a major difficulty because to their abstract and complex character. Numerous methods have been developed to address this challenge. The goal of this work is to find undiscovered exact solitary wave solutions for specific nonlinear partial differential equations that occur in the setting of optical fiber communications and wave propagation. In particular we examine three soliton equations, namely The Stochastic Nizhnik-Novikov-Veselov (SNNV) sys tem models, The Fractional shallow water wave phenomena (Fswwp), and Sch¨afer-Wayne Equation. These models depict a variety of physical events and are well-known for their richness in nonlinear wave propagation. We solve these models using the Extended Mod ified Auxiliary Equation Method (EMAEMM), a novel and effective method for handling nonlinear partial differential equations (NLPDEs). The primary goal of this research is to develop new precise solutions and graphical representations which created with Mathemat ica and Maple, we examine the stability, bifurcation, chaotic behavior, and sensitivity of the resulting solitons. These include 2D and 3D plots, density linear plots, 1D slice con tour plots, stream density plots, 2D-3D phase portraits, Poincar´e phase diagrams, and time series phases.