Stochastic solitons in a two-layer fluid system

Abstract

In this paper, stochastic one- and two-soliton solutions for the stochastic Benjamin–Ono equation modeling the nonlinear random waves in a two-layer fluid system with and without the uneven bottom topography are derived via the Gaussian white noise functional approach and the Hirota method. The effects of Gaussian white noise on the propagation and the interaction of the stochastic solitons are discussed. In the stochastic-one-soliton case, impact on the velocity is enlarged with the increase of the intensity of Gaussian white noise while the soliton amplitude and shape keep unchanged during the propagation. We also investigate the results of the stochastic-two-soliton interaction and the effects of Gaussian white noise on the interaction of stochastic two solitons. With the increase of Gaussian white noise, the velocity of two solitons causes the corresponding change, while the soliton amplitudes and shapes keep unchanged before and after the interaction. • Successfuly obtaining the stochastic one-soliton, two-soliton and N-soliton solutions of the stochastic Benjamin–Ono equation. • Investigating the effect of Gaussian white noise on propagation and interactions of the stochastic solitons. • The impact on the velocity can be greater as the intensity of Gaussian white noise increases in the stochastic one-soliton case. • The amplitude keep unchange along the propagation in the stochastic one-soliton case. • There is a change over the velocities of the stochastic two solitons when there exists white noise.