Certain mathematical models of wave dynamics of the shelf zone are presented. Numerical solutions demonstrating new characteristic effects of the interaction between nonlinear water waves and the bottom topography are obtained. Nonlinear dispersive asymptotic approximations describing the propagation of waves above the bottom topography are obtained on the basis of an exact two-dimensional formulation that includes the Laplace equation for the velocity potential, nonlinear conditions on the free surface and conditions at the bottom surface. This is done on the assumption that dispersion parameter β and gradient γ of the bottom surface are small, whereas nonlinearity factor α is assumed to be arbitrary, unlike the extensively employed traditional approximate theories. A nonlinear model for investigating the motion of saline sea water and also the restructuring of an irregularly shaped bottom by means of waves propagating above it are also presented. The corresponding initial- and boundary-value problem is solved by the method of finite differences for specified semisinusoidal-type pulses repeatedly generated at the inlet. In addition, this problem is analyzed on the basis of the KdV equation with a specified inlet soliton. Numerical results are presented and analyzed.
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