K. Matsuba et K. Nozaki, RENORMALIZATION-GROUP METHOD AND REDUCTIVE PERTURBATION METHOD, Journal of the Physical Society of Japan, 66(11), 1997, pp. 3315-3317
It is shown that the renormalization group method does not necessarily
eliminate all secular terms in the perturbation series to partial dif
ferential equations. Also, choosing a subspace of renormalizable secul
ar solutions corresponds with setting scales of independent variables
in the reductive perturbation method.