Stochastic dark solitons for a higher-order nonlinear Schrödinger equation in the optical fiber

Abstract

In this paper, a stochastic higher-order nonlinear Schrödinger equation, which describes the wave propagation in the optical fiber with stochastic dispersion and nonlinearity, is investigated analytically. Via the symbolic computation and white noise functional approach, the stochastic dark one- and two-soliton solutions are obtained, and effects of the Gaussian white noise on the stochastic dark one and two solitons are discussed. For the stochastic dark one soliton, velocity and phase change randomly because of the Gaussian white noise, but the energy, shape and amplitude keep unchanged during the soliton propagation. For the stochastic dark two solitons, effect of the Gaussian white noise leads to the inversion of the velocity directions, while the velocities have the same varying trend so that the interaction appears that the stochastic dark two solitons keep parallel.