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.

A new parabolic equation for propagation of weakly nonlinear Stokes waves over uneven bottom;

Through simplification on the modified third-order evolution equations for weakly nonlinear water waves propagating over uneven bottoms, a new mild slope equation and a new paraboic wave equation are derived.

Study on the Generation and Evolution of the Nonlinear Wave on Uneven Bottoms;