A Geometrical Formulation of the Renormalization Group Method for Global Analysis II: Partial Differential Equations

It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations are analyzed. The amplitude equations which are usually derived by the reductive perturbation theory are shown to be naturally derived as the equations describing the envelopes of the local solutions obtained in the perturbation theory.