  A Hamiltonian model for the propagation of internal water waves interacting
with surface waves, a current and an uneven bottom is examined. Using the
so-called Dirichlet-Neumann operators, the water wave system is expressed in
the Hamiltonian form, and thus the motions of the internal waves and surface
waves are determined by the Hamiltonian formulation. Choosing an appropriate
scaling of the variables and employing the Hamiltonian perturbation theory from
Hamiltonian formulation of the dynamics, we derive a KdV-type equation with
variable coefficients depending on the bottom topography to describe the
internal waves.
