  We present a one-parameter family of mathematical models describing the
dynamics of polarons in linear periodic structures such as polypeptides. By
tuning the parameter, we are able to recover the Davydov and the Scott models.
We describe the physical significance of this parameter. In the continuum
limit, we derive analytical solutions which represent stationary polarons. On a
discrete lattice, we compute stationary polaron solutions numerically. We
investigate polaron propagation induced by several external forcing mechanisms.
We show that an electric field consisting of a constant and a periodic
component can induce polaron motion with minimal energy loss. We also show that
thermal fluctuations can facilitate the onset of polaron motion. Finally, we
discuss the bio-physical implications of our results.
