Propagation of magnetic solitary waves in inhomogeneous ferrites, subjected to damping effects

Abstract

We pay particular interest to the dynamics of solitary wave in magnetic insulators, while taking into account inhomogeneous exchange and damping effects simultaneously. We carry out our investigations in the windings of the work previously carried out by the authors (Tchidjo et al., 2019). We first of all derive a new solution of the system of our interest by direct calculus. Since in the previous analysis, the amplitude of the wave were fixed so that influence of the inhomogeneous term was acting principally on the width of the wave, we here proceed to different analysis, which consist in bringing more information on the contribution of the inhomogeneous term on the dynamics of waves in ferrites. We show that, while considering the full impact of the inhomogeneous term acting on the amplitude of the wave and on the phase simultaneously, one understands that there are two types of inhomogeneities that can be recognized by their effects. The first has as effect to increase the amplitude of the wave and in the same time reduce its width, while for the other type of inhomogeneity, the reverse process is observed. We provide analytical expression of the energy of the system under current interest and, as a result, it appears clearly that in both cases, energy density of the system is fully conserved. Therefore, we show that the only term that is responsible of slowing down the energy during the motion of magnetic wave is just the damping parameter.