Retrieval of optical soliton solutions of stochastic perturbed Schrödinger-Hirota equation with Kerr law in the presence of spatio-temporal dispersion

In this study, for the first time, a study on optical soliton solutions of the stochastic perturbed Schrödinger-Hirota equation which models the propagation of solitons through optical fibers having the Kerr law is carried out. For this purpose, the nonlinear partial differential equation of the examined model is first reduced to the nonlinear ordinary differential equation form using the complex wave transformation. Then, using the new Kudryashov and the Kudryashov methods, bright, dark and singular soliton solutions are derived as a basic step. The next part is devoted to the examination of the noise effect, and first of all, soliton solutions are obtained in the absence of noise strength. Afterwards, the same soliton solutions are obtained, taking into account the noise effect, and comparison and comments are made. In addition to the fact that the form of the examined equation has not been presented and studied before. Considering that, in today’s world, taking into account the effect of noise is an inevitably important factor for engineering models to be designed correctly and to operate efficiently, it is obvious that the results obtained will contribute to the literature.