Remarks on parametric resonance of neutrino oscillations in the earth

Neutrino oscillations in matter can exhibit a specific resonance enhancement -- parametric resonance, which is different from the MSW resonance. Recently it has been shown that the oscillations of atmospheric and solar neutrinos inside the earth can undergo parametric enhancement when neutrino trajectories cross the core of the earth. In this paper we continue the study of the parametric resonance of neutrino oscillations in the earth. The following issues are discussed: stability of the resonance with respect to the variations of the zenith angle of the neutrino source; higher-order resonances; prospects of the experimental observation of the parametric resonance of neutrino oscillations. We also comment on a recent controversy regarding the physical nature of the resonance enhancement of the oscillations of the core crossing neutrinos in the earth