Executive Summary : | The project focuses on transmission line theory in electrical engineering, focusing on nonlinear wave dynamics in networks. Researchers use the nonlinear schrödinger (NLs) equation to understand wave phenomena. A notable discovery is rogue waves (RWs), which pose risks to electronic components. Coupled electric transmission lines (CETLs) gain attention for practical applications. The modified Naguchi model examines dispersive elements and external potentials, deriving NLs equations revealing rogue wave behavior. The study also explores second-neighbor interactions in one-dimensional electrical transmission lines, leading to the cubic-quintic NLs equation. The project also delves into modulational instability, a fundamental mechanism underlying rogue wave formation in nonlinear systems. The study investigates the transition from constant backgrounds and plane wave solutions to continuous wave backgrounds, shedding light on differences in instability rates and behaviors. |