The splitting and mixing of two spin branches of Caroli-de Gennes-Matricon states in non-axisymmetric cores of $^3$He-B vortices is the source of the nonlinearity of the spectrum: the discrete levels of the core fermions are slightly non-equidistant. This nonlinearity leads to phenomenon, known as the frequency comb -- the periodic in frequency response to external perturbation.

The period of frequency comb is by several orders of magnitude smaller than the distance between the discrete levels of the core fermions, which suggests to probe the core states using NMR technique. Recent NMR experiments with Bose-Einstein condensate of magnons, which are localized in magnetic-textural trap in $^3$He-B, demonstrated that attenuation of magnon BEC in the presence of vortices is caused by resonance absorption by the oscillating asymmetric vortex cores. Moreover, in the presence of vortices the relaxation time of magnon BEC is periodic in frequency with period ~ 1 kHz. This magnitude is consistent with the period of the frequency comb due to Caroli-de Gennes-Matricon states (Majorana fermions). However, the observed dependence of the period of oscillations on magnetic field does not support this interpretation, and the source of oscillations remains unclear.