We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena are RG equations. The renormalized perturbation approach may be simpler to use than other approaches, because it does not require the use of asymptotic matching and yields practically superior approximations.

• Received 13 June 1994

DOI:https://doi.org/10.1103/PhysRevLett.73.1311