  The classical equation of motion of a Davydov model in a coherent state
approximation is analyzed using the multiple scales method. An exponentially
decaying long range interaction (Kac-Baker model) was included. In the first
order, the dominant amplitude has to be a solution of the nonlinear
Schroedinger equation (NLS). In the next order, the second amplitude satisfies
an inhomogeneous linearized NLS equation, the inhomogeneous term depending only
on the dominant amplitude. In order to eliminate possible secular behaviour the
dominant amplitude has to satisfy also the next equation in the NLS hierarchy
(a complex modified KdV equation). When the second order derivative of the
dispersion relation vanishes, the scaling of the slow space variable has to be
changed, and a generalized NLS equation with a third order derivative is found
for the dominant amplitude.
  As the coefficient of the third derivative is small, a perturbational
approach is used to discuss the equation. A complete solution is given when the
dominant amplitude is the one-soliton solution of the NLS equation.
