# Optical soliton perturbation with complex ginzburg–landau equation having multiplicative white noise and nine forms of self–phase modulation structures

## TL;DR

This paper explores how optical solitons behave under noise in a nonlinear optics model, showing that their amplitude remains stable despite phase changes.

## Contribution

The study introduces nine new self-phase modulation structures and demonstrates soliton robustness against noise using an analytical method.

## Key findings

- White noise primarily affects soliton phase without altering amplitude.
- Nine self-phase modulation structures exhibit unique nonlinear and dispersive behaviors.
- The generalized G′/G-expansion method successfully derives exact soliton profiles.

## Abstract

This paper investigates new optical soliton solutions to the complex Ginzburg–Landau equation in the presence of white noise, a fundamental model in nonlinear optics that describes soliton dynamics. The study focuses on nine distinct forms of self-phase modulation structures, each exhibiting unique nonlinear characteristics and dispersion properties. To derive the soliton solutions, the generalized G′/G-expansion approach is employed, which is known for its effectiveness in handling nonlinear differential equations and extracting exact solutions systematically. Through this analytical framework, a variety of soliton profiles are retrieved, demonstrating the influence of nonlinear dispersion and gain-loss terms on soliton propagation. A key observation from the analysis is that the presence of white noise primarily affects the phase component of the solitons, while their amplitude remains intact. This result suggests that the robustness of the soliton amplitude against stochastic perturbations could have significant implications for practical optical communication systems and laser pulse propagation, where maintaining stable intensity profiles is crucial. The obtained results provide valuable insights into the interplay between noise and nonlinear wave dynamics, offering potential applications in fiber-optic communication, mode-locked lasers, and other areas of photonics where controlled soliton evolution is essential.•The paper investigates optical soliton solutions of the complex Ginzburg–Landau equation with white noise, focusing on nine forms of self-phase modulation with varied nonlinear and dispersive properties.•Using the generalized G′/G -expansion method, the study derives exact soliton profiles, revealing how nonlinear dispersion and gain-loss mechanisms shape soliton dynamics.•A key finding shows that white noise affects soliton phase without disturbing amplitude, highlighting amplitude robustness with implications for optical communications and laser systems.

The paper investigates optical soliton solutions of the complex Ginzburg–Landau equation with white noise, focusing on nine forms of self-phase modulation with varied nonlinear and dispersive properties.

Using the generalized G′/G -expansion method, the study derives exact soliton profiles, revealing how nonlinear dispersion and gain-loss mechanisms shape soliton dynamics.

A key finding shows that white noise affects soliton phase without disturbing amplitude, highlighting amplitude robustness with implications for optical communications and laser systems.

Image, graphical abstract