Analogous Hawking Effect in Dielectric Media and Solitonic Solutions

We review some aspects of our longstanding research concerning the analogous Hawking effect in dispersive dielectric media. We introduce nonlinear contributions in the polarization field in the relativistically covariant version of the Hopfield model and then, in order to provide a simplified description aimed at avoiding some subtleties in the quantization of the original model, we discuss the so-called $phipsi$-model. We show that the nonlinearity allows for introducing in a self-consistent way the otherwise phenomenological dependence of the susceptibility and of the resonance frequency $omega_0$ on the spacetime variables, and this is a consequence of the linearization of the model around solitonic solutions representing propagating perturbations of the refractive index, to be then associated with the Hawking effect.