Nonlinear model for wave propagation

Employing the Hamitonian theory, the canonical equations of water waves is used to derive a nonlinear model. In this paper, a unified non-linear model for water wave propagation is presented. This model can be simplified to the mild-slope equation in the linear case. It is consistent with Stokes wave theory when water depth is deep and reduces to an equation of Boussinesq's type in shallow waters. Results of numerical computations of nonlinear water waves propagating over a submerged bar and a rectangular step are also presented in one-dimensional case. Nonlinear behaviors of water waves are captured, but further works are needed.