A numerical analysis of the behaviour of the Galerkin equations relevant to electromagnetic wave propagation in nonlinear media

The electromagnetic scattering of a normal incident monochromatic plane wave from a “strongly” nonlinear dielectric slab is considered. The time dynamic of the field inside the nonlinear body is studied by means of the Galerkin method. The solutions of the Galerkin equations are calculated using the fourth-order Runge-Kutta-Nystrom method. Their asymptotic behaviour abruptly changes its qualitative properties by continuous variation of the system parameters and a surprising wealth of different nonlinear phenomena appears. They are: bifurcation of the periodic response, subharmonic, almost-periodic solutions and chaotic dynamics