Wick-Type Stochastic Fractional Solitons Supported By Quadratic-Cubic Nonlinearity

When a random environment with the Gaussian white noise function is considered, the Wick-type stochastic fractional quadratic-cubic nonlinear Schrödinger equation is used to govern the propagation of optical pulse in polarization-preserving fibers. Using a new strategy, namely combining the variable-coefficient fractional Riccati equation method with the fractional derivative, Mittag–Leffler function and Hermite transformation, some special fractional solutions with the Brownian motion function including fractional bright and dark solitons, and fractional combined soliton solutions are given. Under the influence of the stochastic effect from the stochastic Brownian motion function portrayed by using the Lorentz chaotic system, some wave packets randomly appear during the propagation, and thus make fractional bright soliton travel wriggled in the both periodic dispersion system and the exponential dispersion decreasing system. However, the stochastic Brownian motion function has a more significant impact on the propagation of fractional bright soliton in the periodic dispersion system than that in the exponential dispersion decreasing system.