Analyzing the impact of white noise on optical solitons and various wave solutions in the stochastic fourth-order nonlinear Schrödinger equation
Mohammed F. Shehab, Hamdy M. Ahmed, Salah Boulaaras, M.S. Osman, Karim K. Ahmed
Abstract
We derive novel soliton solutions and additional wave solutions for the stochastic nonlinear Schrödinger equation with fourth-order perturbations. The study employs an enhanced modified extended tanh-function approach that provides many solution types. These solutions comprise singular, bright, and dark solitons. Furthermore, solutions for Jacobi elliptic functions, Weierstrass elliptic functions, hyperbolic solutions, periodic solutions, and singular periodic solutions are established. This approach provides a useful and efficient way to find accurate stochastic solutions for a range of nonlinear stochastic partial differential equations. A significant gap in the current theoretical approaches is filled by the analysis, which guarantees a comprehensive and non-redundant base of solutions. The impact of the noise is illustrated graphically using examples of the recovered solutions with varying noise levels. The optical solitons produced in respect to this form have never been explored by the proposed technique before, and the results have never been published.