Extraction of Solitons Emerging in Nonlinear Dynamics

Abstract

The extraction of solitons that emerge in nonlinear dynamics is examined in this thesis, with particular attention to two significant models: the Perturbed Chen-Lee-Liu and the Biswas Milovic models. These models, which are renowned for their complexity in nonlinear wave propagation, describe a wide range of physical phenomena. The Extended Modified Auxil iary Equation Method (EMAEMM), a powerful yet efficient method for resolving nonlinear partial differential equations (NLPDEs), is used to derive solution solutions to these mod els. The EMAEMM method is a useful tool in nonlinear analysis as it makes it easier to find exact solutions by breaking down the equations into simplified forms. The ability of soliton to hold its shape during propagation makes it useful in a variety of applications, including fluid dynamics, optical fibers, and plasma physics. The stability and sensitivity of the resulting solitons is examined, and a number of graphical representations—all gen erated via Mathematica—are shown, including 2D, 3D, density linear, 1D, slice contour plotting, and stream density plots. The observed solitons exhibit a wide variety of behav iors and include bright, dark, kink, periodic, and optical solitons. Insights into the stability and representation of solitons in mathematical physics are provided by this comprehensive examination of soliton dynamics in nonlinear systems.