STOCHASTIC BENJAMIN-ONO-EQUATION AND ITS APPLICATION TO THE DYNAMICS OF NONLINEAR RANDOM WAVES

The stochastic Benjamin-One equation is introduced, which models the p ropagation of nonlinear random waves in a two-layer fluid system with and without uneven bottom topography. In the case of the flat bottom, the effect of the external random flow field on the evolution of both soliton and periodic wave is investigated. In particular, the mean val ue and the correlation function of these nonlinear wave fields are cal culated exactly under the assumption that the flow held obeys the Gaus sian stochastic process with a white noise. It is found that in the li mit of large time, the mean value of an algebraic soliton approaches a Gaussian wave packet whereas that of a periodic wave is represented b y Jacobi's theta function. In the case of the uneven bottom, a perturb ation analysis is performed to evaluate the mean value of an algebraic soliton under the influence of random change of bottom topography. Th e large time asymptotic of the soliton is shown to exhibit a Gaussian wave packet with a small amount of the phase shift caused by the inter action between the soliton and the random bottom topography.