Traveling wave solutions, stability analysis, and chaotic behavior of the stochastic nonlinear Schrödinger equation with multiplicative white noise and spatio-temporal dispersion

Abstract This paper primarily investigates the stochastic nonlinear Schrödinger equation with multiplicative white noise and spatio-temporal dispersion. The model describes ultrashort pulse propagation through random media in nonlinear optics, where spatio-temporal dispersion originates from refractive index anisotropy, and multiplicative noise reflects environmental fluctuations modulating nonlinear coefficients. We analyze its dynamical properties and employ dynamical system theory along with the polynomial complete discriminant system to derive its traveling wave solutions, including elliptic function periodic solutions, rational function solutions, and implicit solutions. Additionally, numerical simulations are conducted to visualize the traveling wave solutions under specific parameters, and the influence of noise intensity on these solutions is examined. Furthermore, we incorporate an external perturbation term to examine the chaotic dynamics of the equation, investigating the chaotic behavior of solutions through phase portraits and Lyapunov exponent. Finally, we explore the sensitivity of the equation under different initial conditions for specific parameter values. These findings may provide valuable insights for applications in nonlinear optics and communication systems.