Stochastic optical solitons in nonlinear media type Kerr

In this work we present a deduction of the one dimensional stochastic non-linear Schrodinger equation (SNLSE). We have assumed that the material where the optical beam is propagated has a Kerr type nonlinearity. We have deducted the SNLSE from the Maxwell equations by adding in the complex electric field, random noise with Gaussian distribution. We analyzed the modified NLSE and we compared it against the deterministic NLSE.