Characterizing stochastic solitons behavior in (3+1)-dimensional Schrödinger equation with Cubic–Quintic nonlinearity using improved modified extended tanh-function scheme

An extended version of (3+1)-dimensional non-linear Schrödinger equation that has a cubic–quintic nonlinear component under the stochastic effects is examined in this investigation. Several stochastic exact solutions of this model is acquired through the application of the improved modified extended tanh-function scheme (IMETFS). This method offers a practical and effective approach to finding precise solutions to several kinds of nonlinear partial differential equations. In addition, these solutions include stochastic soliton solutions (bright, singular, combo dark-singular), and exact solution such as singular periodic, Jacobi elliptic function, Weierstrass elliptic doubly periodic solution, rational, and exponential functions. Since it is the first study of its sort to examine multiplicative white noise’s impacts in this particular setting, it offers fresh insights and innovative research approaches for the field’s future studies. The work adds much to our understanding of soliton theory and how it relates to optical fiber technology while illuminating hitherto unknown facets of multiplicative white noise. To illustrate the impact of the noise, a few recovered solutions with varying noise strengths are given graphically as examples.