Optical soliton solutions of the stochastic generalized nonlinear Schrödinger equation with arbitrary refractive index in Itô sense

This paper introduce the stochastic generalized nonlinear Schrödinger equation (SGNLSE), which includes a stochastic term proportional to a Wiener process and models random refractive index variations in the Itô sense. This paper derives optical soliton solutions to the SGNLSE using the generalized Jacobi-elliptic function method. We investigate soliton solutions for $$M=1$$ , periodic wave solutions for $$M=0$$ , and Weierstrass elliptic function (WEF) solutions. The paper also discusses the physical implications of these solutions, particularly in the fields of nonlinear optics and plasma physics, where both stochastic perturbations and nonlinear effects significantly influence the dynamics of wave propagation. By exploring these solutions, this paper provides valuable insights into the combined effects of nonlinearity and randomness on wave propagation, which is important for understanding the behavior of complex systems where both deterministic and stochastic forces are at play.