Stochastic soliton solutions for the (2+1) -dimensional stochastic Broer–Kaup equations in a fluid or plasma

In this paper, we investigate the (2+1) -dimensional stochastic Broer–Kaup equations for the shallow water wave in a fluid or electrostatic wave in a plasma. Through the symbolic computation, Hirota method and white noise functional approach, the stochastic one- and two-soliton solutions are derived. Through the stochastic one soliton solutions, we derive the velocities of solitons, respectively, and graphically investigate the effect of the white noise on the velocities. The effects of the Gaussian white noise on the dynamic properties of the solitons are discussed. We get that the white noise poses some influence to the soliton of U, where U is related to the horizontal velocity of the water wave, with which the soliton of U would vanish with time instead of propagating stably. On the contrary, transmission of the soliton of V presents certain stability no matter whether the white noise exists, where V is related to the horizontal elevation of the water wave. Figures are displayed for the elastic collisions between the two oscillating-, parabolic- and bell-type solitons, respectively. In addition, collisions are shown to be elastic through the asymptotic analysis.