On the propagation of nonlinear waves through a medium endowed with a periodic structure

The propagation of nonlinear waves through a medium endowed with a periodic structure is theoretically studied using a simple perturbation method, and in order to confirm the result, the reflection coefficient of the wave's energy is numerically calculated. It is shown that the reflection coefficient depends on the wave amplitude, and this fact can be explained from the characteristic behavior of the pseudo-unstable state solution and the doubly-periodic stable state solution. These concepts were previously proposed by the present author in a study of the nonlinear Mathieu equation.