  Magnetic skyrmions in bulk crystals are line-like topologically protected
spin textures. They allow for the propagation of magnons along the skyrmion
line but are localized inside the skyrmion line. Analogous to the vortex line,
these propagating modes are the Kelvin modes of a skyrmion line. In crystals
without an inversion center, it is known that the magnon dispersion in the
ferromagnetic state is asymmetric in the wavevector. It is natural to expect
that the dispersion of the Kelvin modes is also asymmetric with respect to the
wavevector. We study the Kelvin modes of a skyrmion line in the ferromagnetic
background. In contrast, we find that the lowest Kelvin mode is symmetric in
the wavevector in the low energy region despite the inversion symmetry
breaking. Other Kelvin modes below the magnon continuum are asymmetric, and
most of them have a positive group velocity. Our results suggest that a
skyrmion line can function as a one-way waveguide for magnons.
