© 2022 Elsevier GmbHPurpose: This study aimed to examine the effects of the parameters, the group velocity dispersion (GVD), the third-order dispersion (3OD), spatio-temporal dispersion (STD), the third-order spatio-temporal dispersion (TO-STD), self-steepening effect and nonlinear dispersions terms, included in the equations modeling optical fiber phenomena on the optical solitons. Therefore, the aim of this study is not to apply a method to derive different types of optical soliton solutions and their graphical representation. For this purpose, the Biswas–Arshed equation, which is the important equation to model to compensate for the effects of dispersion in the case of nonlinearity and to provide the necessary balance for soliton propagation to continue, is investigated by utilizing the new Kudryashov approach. Methodology: First, the nonlinear ordinary differential (ODE) form of the investigated problem was obtained by using the complex wave transform. Afterward, a linear equation system was created using the new Kudryashov scheme, the appropriate solution sets were found, and the bell-shaped soliton, which was desired to be examined, was obtained by using these sets and selecting the suitable parameter values. Depending on the definition of the Biswas–Arshed equation and the constraints of the method, two-dimensional graphical views were obtained, and necessary comments were made to better observe the effect by giving different values to the parameters whose effect is desired to be examined. Findings: At the end of the detailed examination, important and fundamental findings were obtained. Such that the model parameters do not only consist of a set of numerical values that can be given to obtain various soliton graphics, but also, the model parameters have a crucial effect on the soliton behavior. In addition, parameter values should be determined by evaluating both each other and the physical design of the investigated equation. Originality: This study, which examines the effects of model parameters on the behavior of the Biswas–Arshed equation on the behavior of bell shape soliton, is presented for the first time in this article.