Characterizing Localized Wave Structures in High-Dimensional Nonlinear PDEs

Abstract

This thesis investigates the extraction of solitons that arise in nonlinear dynamics, focus ing on two important models: the Stochastic Davey–Stewartson equation and the Ben jamin–Bona–Mahony (BBM) equation well known Nonlinear Evolution equation. Numer ous physical events are described by these models, which are well known for their intricacy in nonlinear wave propagation. These models are solved using the Extended Modified Aux iliary Equation Method (EMAEMM), a potent yet effective technique for resolving nonlin ear partial differential equations (NLPDEs). By simplifying the equations, the EMAEMM approach facilitates the search for precise solutions, making it a valuable tool in nonlinear analysis. Optical fibers, fluid dynamics, and plasma physics are just a few of the many applications that benefit from the soliton’s ability to maintain its shape while propagating. A variety of graphical representations, all created using Mathematica, are displayed, in cluding 2D, 3D, density linear, 1D, slice contour plotting, and stream density plots, and the stability and sensitivity of the resulting solitons are investigated. Bright, dark, kink, periodic, and optical solitons are among the many different behaviors of the reported soli tons. This thorough analysis of soliton dynamics in nonlinear systems offers insights on the stability and representation of solitons in mathematical physics