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.

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

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.

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