  For a class of scalar partial differential equations that incorporate
convection, diffusion, and possibly dispersion in one space and one time
dimension, the stability of traveling wave solutions is investigated. If the
initial perturbation of the traveling wave profile decays at an algebraic rate,
then the solution is shown to converge to a shifted wave profile at a
corresponding temporal algebraic rate, and optimal intermediate results that
combine temporal and spatial decay are obtained. The proofs are based on a
general interpolation principle which says that algebraic decay results of this
form always follow if exponential temporal decay holds for perturbation with
exponential spatial decay and the wave profile is stable for general
perturbations.
