From optical solitons to chaos: stochastic dynamics in nonlinear Schrödinger systems

This paper considers the stochastic nonlinear Schrödinger equation with Brownian motion for the representation of noise effects in the propagation of waves. Using the modified Sardar sub-equation method, exact solutions of the solitons and periodic type are constructed. The effect of stochastic perturbation on the solutions is studied revealing the formation of deformations and instabilities. The chaotic nature of the system is further verified under the effects of sinusoidal, cosine, hyperbolic, and Gaussian perturbations through numerical experiments. Phase diagrams and time series show a very complex non-periodic pattern. Sensitivity to the initial condition proves that the solution is highly sensitive to changes in the initial values.