In this paper,interfacial internal waves in N-layer density-stratified fluid with background current were investigated by using a perturbation method,and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial internal waves were presented based on the small amplitude wave theory.

Here, a n-layer fluid evolution system, with constant density and uniform horizontal current velocity in each layer with a thickness consisting of undisturbed and disturbed part, over uneven moving bottoms is developed to illustrate the Hamiltonian description.