Exact noise influenced soliton solutions of a high-order stochastic nonlinear Schrödinger equation with weak nonlocal nonlinearity in a non-Kerr medium

Abstract In this study, a high-order stochastic nonlinear Schrödinger equation (SNLSE) with weak non-local nonlinearity in a non-Kerr law medium is investigated. This model describes the propagation of solitons in nonlinear optical fibers under stochastic effects and higher-order nonlinear interactions. To obtain analytical solutions, a wave transformation together with symbolic computations and the modified extended mapping method (MEMM) is employed. As a result, various exact wave solutions are derived, including bright, dark, singular, periodic, and rational-type solitons. A rigorous linear stability analysis is performed using perturbation theory and dispersion relation analysis, demonstrating that the obtained solutions are linearly stable under small perturbations. The graphical behavior of the solutions under different parameter settings is also presented to illustrate the dynamical characteristics of the model. The results confirm the efficiency and reliability of the proposed method in handling high-order stochastic nonlinear Schrödinger-type equations.