Akademik Veri Yönetim Sistemi
Engineering Computations (Swansea, Wales), ss.1-15, 2025 (SCI-Expanded, Scopus)
Purpose – The purpose of this article is to explore the optical soliton solutions of the stochastic (2 + 1)-dimensional nonlinear Schrödinger equation (NLSE) with Kerr law media influenced by multiplicative white noise in the Itô sense (mw-Itô). This investigation is conducted using two innovative methods—the new Kudryashov algorithm and the generalized Kudryashov scheme—applied for the first time in this context. By employing wave transformation techniques, the stochastic NLSE with Kerr law media is converted into an ordinary differential equation (ODE). The methods are then used to obtain stochastic soliton solutions, which include bright, dark, and singular soliton forms. The article also includes 2D and 3D visualizations to interpret the physical behavior of these solutions. Additionally, the impact of noise on the (2 + 1)-dimensional NLSE is examined by varying noise effect parameters, with graphical representations provided to illustrate the influence on different soliton types, accompanied by relevant commentary. Design/methodology/approach – The article significantly advances the understanding of optical soliton solutions in stochastic Kerr law media by employing innovative analytical methods. It highlights the importance of noise parameters in shaping the soliton dynamics, making a substantial contribution to the field of nonlinear optics and stochastic processes. Findings – The findings underscore the effectiveness of the new and generalized Kudryashov methods in solving the stochastic (2 + 1)-dimensional NLSE with Kerr law media. The graphical presentations and noise impact analyses provide valuable insights into the physical dynamics of solitons under stochastic influences, contributing significantly to the field of nonlinear optics and stochastic processes. Originality/value – The primary goal of the article is to derive optical soliton solutions for the stochastic (2 + 1)-dimensional nonlinear Schrödinger equation (NLSE) with Kerr law media influenced by multiplicative white noise in the Itô sense (mw-Itô). The article introduces the use of two efficient methods—the new Kudryashov algorithm and the generalized Kudryashov scheme—for this purpose, marking the first application of these methods to this problem. To achieve this, the stochastic NLSE with Kerr law media is transformed into an ordinary differential equation (ODE) using wave transmutation techniques. By applying the properties of the introduced methods, stochastic soliton functions are obtained, which include bright, dark, and singular soliton solutions. The article provides 2D and 3D graphical representations to illustrate the physical behavior of some of the obtained solutions. Additionally, it explores the impact of noise by varying noise effect parameters and examining their influence on the graphs of each soliton type. The graphical presentations are used to offer necessary comments and insights into the noise effects on the soliton dynamics. The originality and value of the article lie in the novel application of the Kudryashov methods to the stochastic (2 + 1)-dimensional NLSE with Kerr law media, providing new insights and solutions in this field.