Research has been conducted on the behavior of solitary waves in various nonlinear equations, including the stochastic resonance nonlinear Schrödinger equation, under the influence of noise and other factors. The studies examine the impact of different types of noise, such as Brownian motion and white noise, on soliton structures and solitary wave behavior. The findings appear to cover a range of related topics in nonlinear optics and dynamics, including soliton solutions and phase plane analysis in different equations.