The one-dimensional propagation of magnetic domain walls in an isotropic, linearly elastic, magnetostrictive material is investigated in the framework of the extended Landau-Lifshitz-Gilbert equation where the effects of a spin-polarized current and a rate-independent dry-friction dissipation are taken into account. In our analysis, it is assumed that the ferromagnet is subject to a spatially uniform biaxial in-plain stress generated by a piezoelectric substrate combined with the former in a multiferroic heterostructure. Moreover, a possible connection between the dry-friction mechanism and the piezo-induced strains is conjectured. By adopting the traveling waves ansatz, the effect of such a stress on the domain wall dynamics is explored in both steady and precessional regimes. In particular, it is proved that the magnetoelastic contribution, while it does not formally modify the classical solution, affects both the propagation threshold and the Walker Breakdown conditions involved in the steady regime, in agreement with recent experimental results. In the precessional regime, it is shown that the existence of a correlation between the piezo-induced strains and dry-friction leads to an upward shift of the domain wall velocity.

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A one-dimensional hyperbolic reaction-diffusion model of epidemics is developed to describe the dynamics of diseases spread occurring in an environment where three kinds of individuals mutually interact: the susceptibles, the infectives, and the removed. It is assumed that the disease is transmitted from the infected population to the susceptible one according to a nonlinear convex incidence rate. The model, based upon the framework of extended thermodynamics, removes the unphysical feature of instantaneous diffusive effects, which is typical of parabolic models. Linear stability analyses are performed to study the nature of the equilibrium states against uniform and nonuniform perturbations. Emphasis is given to the occurrence of Hopf and Turing bifurcations, which break the temporal and the spatial symmetry of the system, respectively. The existence of traveling wave solutions connecting two steady states is also discussed. The governing equations are also integrated numerically to validate the analytical results and to characterize the spatiotemporal evolution of diseases.

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-In this work we formulate a generalized theoretical model to describe the nonlinear dynamics observed in combined frequency-amplitude modulators whose characteristic parameters exhibit a nonlinear dependence on the input modulating signal. The derived analytical solution may give a satisfactory explanation of recent laboratory observations on magnetic spin-transfer oscillators and fully agrees with results of micromagnetic calculations. Since the theory has been developed independently of the mechanism causing the nonlinearities, it may encompass the description of modulation processes of any physical nature, a promising feature for potential applications in the field of communication systems.