Akademik Veri Yönetim Sistemi
Results in Engineering, cilt.28, 2025 (ESCI)
Although the design and implementation of such models are of great importance in physical systems, engineering structures, and fiber optic communications, one of the most important issues regarding the design of such models is the noise effect. Studies on the effects of noise in terms of such models have been an area of interest for many researchers in recent years, and there is no doubt that such studies are also an area of interest for researchers conducting experimental studies. This article examines the optical soliton solutions of the stochastic perturbed quintic Gerdjikov-Ivanov equation (namely DNLSIII equation) with spatio-temporal dispersion via the new Kudryashov integration algorithm. The study consists of three main stages. First, an investigation of the proposed model without noise effect, and obtaining the dark and bright solitons. Second, to show that the dark and bright solitons, which form the basis of noise effect investigation, are stable with the help of the Vakhitov-Kolokolov stability criteria (VKSC). And thirdly, consideration of the first scenario with noise effect, and to observe the impact of noise on bright and dark soliton behavior. Analytical solutions of nonlinear partial differential equations and stochastic nonlinear partial differential equations, which model many physical phenomena in engineering and nonlinear optics, are undoubtedly important. However, for these solutions to be physically meaningful, they must first be stable. In this respect, the study will make a small contribution to research in this field by examining the perturbation-involved form of the Gerdjikov-Ivanov equation, an important model for nonlinear optics, from a stochastic perspective. It will also obtain the bright and dark soliton forms, which are also important forms for nonlinear optics, using the Kudryashov method, an effective method. It will also demonstrate the stability of the obtained solutions using the VKSC, another effective analysis technique, and then examine the effects of noise. Considering that such mathematical and theoretical investigations and studies are often a resource for researchers working experimentally, the presented findings will contribute to research in this field, albeit modestly.