<p>This article investigates the traveling wave solutions to the Schrödinger–Hirota equation in birefringent fibers with differential group delay and multiplicative white noise. Through traveling wave transform, the equation is transformed into the planar dynamical system, and the type of solutions is predicted by combining the knowledge of bifurcation theory. Subsequently, different perturbations are added to the dynamical system, resulting in different chaotic behaviors. To our knowledge, this is the first time that chaotic behavior has been introduced into this model. By using the complete discriminant system of the polynomial method, more forms of traveling wave solutions of the model are obtained. The topological stability of these solutions is analyzed. A novel finding of this study compared to previous studies is that the random averaging of solutions destroys the soliton and periodic features, while the non-averaged solution preserves these features. These features can be clearly observed from the images.</p>