The current paper recovers dispersive optical solitons in birefringent fibers that are modeled by the Schrödinger–Hirota equation with differential group delay and white noise. Itô Calculus conducts the preliminary analysis. The (G 0/G)-expansion approach and the enhanced Kudryashov’s scheme gave way to a wide spectrum of soliton solutions with the white noise component reflected in the phase of the soliton.