By combining the hydraulics and hydrology method,three mathematic models of the dynamic wave,the nonlinear kinematic wave and the multilinear Muskingum method are developed and the key issues of these models are expatiated particularly in this paper.

Considering current and wave loads, hydrodynamic force is evaluated at the instantaneous position for the ATP by Morison formula, the highly nonlinear motion equation is established by Lagran.

Considering current and wave loads,and hydro-dynamics acted on the ATP at the instantaneous position is calculated by Morison formula,the highly nonlinear motion equation is established by Lagrange principle.

The highly nonlinear motion equation is established by Lagrangian Equations considering coulomb friction,and viscous structural damping as well as the nonlinear fluid dynamics of current.

The nonlinear waves of inviscid fluids in an elastic tube are studied.

In this paper,the higher-order asymptotic solution to the Cauchy problem of a nonlinear wave equation is found by using a computer algebra-perturbation method.

The stationary probability density function (PDF) and the stationary mean out-crossing rate (MOR) of the response of ship nonlinear roll-motion subjected to additive stochastic white noise excitation are examined by a new approximate method in this paper.