We study the existence, uniqueness, regularity and continuous dependence
on initial data of solutions for the Cauchy problem associated with the
coupled system of Boussinesq type equations forced by highly oscillatory
smooth coefficients. The model considered describes two-way propagation
of long water waves with small amplitude on the surface of a one-dimensional
channel with rough bottom (disordered topography). The dependent variables
in this model are the wave n elevation and the potential velocity
u measured at the fixed depth Z0 = square root of 2/3.