Investigation of nonlinear dynamics in the stochastic nonlinear Schrödinger equation with spatial noise intensity

This study investigates the stochastic non-linear Schr & ouml;dinger equation (SNLSE) with spatialnoise intensity. Exact solutions, including trigonomet-ric, rational, hyperbolic, periodic, dark, kink, anti-kink, and exponential forms, are achieved by uti-lizing the logarithmic transformation, the(G ' G,1G)-expansion method, and the generalized Kudryashovmethod(gKM).Thesesolutionsareimportantforappli-cations in nonlinear optical fibers, signal processing,communication, and engineering sciences. The effectsof multiplicative noise on these solutions are analyzedthrough 3D, and contour visualizations by utilizingMathematica 11. Moreover, the nonlinear dynamicsof the system are analyzed by using phase portraitswithin bifurcation theory, describing chaotic behaviorinduced by external forces. Chaotic trajectories are fur-ther identified using 2D and 3D plots, time series anal-ysis, and Lyapunov exponents. The model's sensitivityunder varying initial conditions is also examined