Optical soliton perturbation for complex Ginzburg–Landau equation with multiplicative white noise and seven forms of Kudryashov’s self–phase modulation structures

This paper investigates, for the first time, the recovery of optical solitons governed by the perturbed complex Ginzburg–Landau equation with multiplicative white noise. Seven distinct self-phase modulation structures, originally proposed by Kudryashov, are considered to explore the nonlinear dynamics of the system. The study employs the generalized (Formula presented.) -expansion method as the primary integration technique, enabling the derivation of soliton solutions. They are dark, bright, and other types of optical solitons, which are explicitly derived in analytical form. Furthermore, the necessary parameter constraints for the existence of these solitons are systematically derived and discussed. The results contribute to the understanding of soliton dynamics in complex systems influenced by white noise, offering insights into potential applications in nonlinear optics and related fields.