Influence of damping effects on the propagation of magnetic waves in ferrites

In this paper, we study in details the propagation of ultra short waves in magnetic insulators. We discuss the Kraenkel–Manna–Merle (KMM) system, derived from the Maxwell's equations in which damping effects and nonlinearity set in from the first order Landau–Lifshitz–Gilbert equation. We investigate this system analytically, using the well developed inverse scattering transformed method and, as a result the impact of damping effects on the propagation of magnetic waves in ferrites is revealed. We launch our investigations with an integrable system that, under the ultra fast process assumption, approximates the one of our interest which shows that damping acts mostly on the energy of the wave that decrease as time evolves. Such a result is confirmed through some numerical simulations in which analytical and numerical results are matching very goodly. We then conclude on the influence of damping effects on the propagation of waves in magnetic insulators.