  We investigate some aspects of the soliton dynamics in an alpha-helical
protein macromolecule within the steric Davydov-Scott model. Our main objective
is to elucidate the important role of the helical symmetry in the formation,
stability and dynamical properties of Davydov's solitons in an alpha-helix. We
show, analytically and numerically, that the corresponding system of nonlinear
equations admits several types of stationary soliton solutions and that
solitons which preserve helical symmetry are dynamically unstable: once formed,
they decay rapidly when they propagate. On the other hand, the soliton which
spontaneously breaks the local translational and helical symmetries possess the
lowest energy and is a robust localized entity. We also demonstrate that this
soliton is the result of an hybridization of the quasiparticle states from the
two lowest degenerate bands and has an inner structure which can be described
as a modulated multi-hump amplitude distribution of excitations on individual
spines. The complex and composite structure of the soliton manifests itself
distinctly when the soliton is moving and some interspine oscillations take
place. Such a soliton structure and the interspine oscillations have previosly
been observed numerically in [A.C. Scott, Phys.Rev. A 26 578 (1982)]. Here we
argue that the solitons studied by A. Scott, are hybrid solitons and that the
oscillations arise due to the helical symmetry of the system and result from
the motion of the soliton along the $\alpha$-helix. The frequency of the
interspine oscillations is shown to be proportional to the soliton velocity.
