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.

中文翻译：

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二次三次非线性支持的 WICK 型随机分数孤子

当考虑具有高斯白噪声函数的随机环境时，Wick型随机分数二次三次非线性薛定谔方程用于控制光脉冲在保偏光纤中的传播。采用一种新的策略，将变系数分数Riccati方程方法与分数导数、Mittag-Leffler函数和Hermite变换相结合，得到了一些具有布朗运动函数的特殊分数解，包括分数明孤子和分数组合孤子解。给定的。在洛伦兹混沌系统描述的随机布朗运动函数的随机效应的影响下，一些波包在传播过程中随机出现，从而使分数亮孤子在周期性色散系统和指数色散减小系统中蠕动。然而，在周期性色散系统中，随机布朗运动函数对分数亮孤子传播的影响比在指数色散递减系统中更显着。