Fractional optical solitons with stochastic properties of a wick-type stochastic fractional NLSE driven by the Brownian motion

Abstract

A new strategy is proposed to analytically construct stochastic fractional solutions of a wick-type SFNLSE driven from the Brownian motion by altogether using the Hermite transformation, modified Riemann–Liouville fractional derivative rule and fractional mapping method with white noise theory. These stochastic fractional solutions include fractional bright, dark solitons and trigonometric function solutions with or without chirped phase. By the dynamical analysis of stochastic solutions, it is found that the evolution of soliton shows randomness and random wave packets appear. Moreover, the randomness of integer order soliton evolution becomes more obvious compared with fractional solitons. They have discontinuous random phenomena with the evolution of time t, and some random independent wave packets appear. These results will play an important role in the related research on the physical application of the random model in the white noise environment.