Starting with properties of cubic parabola, it is demonstrated elementarily that solving elliptic equations using Jacobian elliptic functions, analytic solutions for a class of nonlinear wave equations and properties of nonlinear waves can be obtained, especially for solitary waves.

In this study, numerical analyses for solving the generalized Biot s dynamic consolidation equations by virtue of finite element method are performed on dynamic response of sandy seabed subjected to non-linear wave loading in the shallow water region.

Based on the generalized formulation of two-dimensional Biot s theory, a finite element numerical method in time domain is developed to evaluate the dynamic response of saturated elastic seabed subject to linear or non-linear wave loadings.

At present, the calculations of wave forces on marine structures are confined to the linear and low-order non-linear wave theories, sometimes these are not satisfied with the requirements.

Chebyshev generalized finite spectral method for linear and nonlinear waves;

A nonlinear wave equation and exact periodic solutions in circular-rod waveguide;

A new pursuit mode of nonlinear wave surface;

Based on the theory of reflection and transmission of electromagnetic wave at a plane boundary,we present the reflection of TM wave on the boundary of media.

From the wave equation of TM wave and the boundary conditions of the electro-magnetic field,An expression of the magnetic field in the three-layer plane waveguide and the derivative expression of theMagnetic field in the direction of y are obtained .

A discussion on the TM modes of isosceles-right triangular waveguide;

According to the principle of superposition,the TE mode and TM mode solution of the boundary value problem in the isosceles-right triangular is discussed in detail for correcting a mistaken solution in some concerning documents and pointing out the proper condition of the method of separation of variables.