The Temporal Variation Laws Of Nonlinear Water Waves

This thesis deals mainly with three aspects of nonlinear water waves:(1) Utilizing the Galerkin cutting spectrum method in the variational equation for fluid, and separating time and space variables, we have obtained the temporal variation laws for finite depth water waves which satisfy the Duffing equation.(2) We consider the case of varying bottom topography. When the varying strength of bottom topography is O(μ6), the temporal variation laws for nonlinear shallow water waves satisfy the non-homogeneous Duffing equation with forcible term which comes from the effect of bottom topography.(3) Taking use of disturbance method, the asymptotic solution for the Duffing equation with the given initial conditions is obtained.