The \(\Phi ^{6}\)-model expansion approach for solving the (2+1)-dimensional NLSE with Kerr law nonlinearity and STD with multiplicative white noise in birefringent fibers

With incorporating of multiplicative white noise, we assess the Itô-coupled NLSE and STD in two and one dimensions with Kerr law nonlinearity and birefringent fibers. Light dynamics in birefringent fibers, including the propagation of soliton waves, the instability of modulation, and the occurrence of stochastic events, all have a connection to this issue. The study aims to facilitate in the growth of fiber lasers, benefiting fields such as in the fields of material processing, medicine, and communications. To achieve this, the \(\Phi ^{6}\) ${\mathrm{\Phi }}^6$ -model approach to expansion is adopted. In addition to Jacobi-elliptic solutions, this work’s analysis also yields dark solitons, bright solitons, singular solitons, and periodic solutions. Because of such results, fiber laser systems in industries like manufacturing, medicine, and communications may be improved upon. The Jacobi-elliptic solution, as well as bright and dark solitons, may be seen in both one- and two-dimensional representations.