Electromagnetic surface waves on a nonlinear dispersive medium

The nonlinear propagation characteristics of electromagnetic surface waves on the interface between a nonlinear isotropic dispersive medium and a vacuum is studied using the method of multiple scales. By this method, a coupled system of semilinear hyperbolic partial differential equations governing the slow variations in the amplitude and phase of a quasi-harmonic electromagnetic surface wave is derived at the third stage of the perturbation expansion. It is shown that these slow variations propagate with the phase velocity of the linear surface wave in the medium. The analysis of the exact solution of the modulation equations reveals that the amplitude grows, remains constant, or decays, depending on whether a certain parameter is positive, zero or negative.