In this paper, we consider the stochastic fifth-order KdV equation, along with its Lax pair, under the influence of Gaussian white noise and Brownian motion. One new result in this paper is that the soliton-periodic mixed solution can be viewed as a novel tool for generating rogue waves when the soliton solution is in the dominant position. By applying the classical Darboux transformation, we obtain analytic solutions to this equation in determinant form. Through detailed analysis of spectral parameters, we construct soliton solutions, periodic solutions, and their mixed solutions for the stochastic fifth-order KdV equation, which incorporates noise terms. We also consider the generalized Darboux transformation and obtain rational solutions to the stochastic fifth-order KdV equation.
Wang et al. (Sun,) studied this question.