  The transport of energy inside protein $\alpha$-helices is studied by
deriving a system of quantum equations of motion from the Davydov Hamiltonian
with the use of the Schr\"odinger equation and the generalized Ehrenfest
theorem. Numerically solving the system of quantum equations of motion for
different initial distributions of the amide I energy over the peptide groups
confirmed the generation of both moving or stationary Davydov solitons. In this
simulation the soliton generation, propagation, and stability were found to be
dependent on the symmetry of the exciton-phonon interaction Hamiltonian and the
initial site of application of the exciton energy.
