Highly dispersive gap solitons with the Kaup–Newell in fiber Bragg grating with white noise effects

This study introduces an innovative examination of the stochastic Kaup–Newell equation within the realm of fiber Bragg grating, signifying a pioneering effort in this area. The study uses two main methods for integration: the [Formula: see text]-expansion method and the enhanced direct algebraic method to find different one-step solutions to the Kaup–Newell equation. The outcomes of this research are multifaceted, revealing an array of optical soliton solutions such as dark, singular, bell-shaped, kink-shaped, bright, and straddled solitons. These findings contribute a novel perspective on the behavior of optical solitons in fiber Bragg gratings, which are essential for optical communications and signal processing. Additionally, applying numerical schemes to these analytically obtained solutions offers a detailed visualization of their characteristics and behaviors, enhancing our understanding of their potential in practical scenarios. This work extends the range of soliton solution types for application and paves the way for subsequent explorations in the field of nonlinear optical systems.