Exploring advanced non-linear effects on highly dispersive optical solitons with multiplicative white noise

This research investigates the dynamics of highly stochastic optical solitons governed by an eighth-order nonlinear Schrödinger equation. The study considers spatio-temporal dispersion effects, higher-order nonlinearity, and multiplicative white noise in the Itô sense. Two robust methods, the singular manifold method and the new generalized exp(-ϕ(ζ)) expansion method, are employed to derive novel closed-form optical soliton solutions. Our exploration of stochastic soliton behavior using Itô calculus sheds light on the influence of multiplicative white noise on the model. Notably, the phase component of the solitons incorporates the white noise, leading to a spectrum of soliton solutions including singular, periodic, singular periodic, combined bright-dark solitons, and various solitary waves. The research provides physical interpretations and visual representations of these solutions through 3D and 2D graphs, using reliable parameter values. Our approach stands out due to the novelty of the problem and the application of untested methods in this context, resulting in numerous new and original optical soliton solutions. These outcomes demonstrate the efficacy of our approach in addressing nonlinear challenges in engineering and the natural sciences, surpassing previous efforts in the literature.