  We apply a multiple-time version of the reductive perturbation method to
study long waves as governed by the shallow water wave model equation. As a
consequence of the requirement of a secularity-free perturbation theory, we
show that the well known N-soliton dynamics of the shallow water wave equation,
in the particular case of $\alpha=2 \beta$, can be reduced to the N-soliton
solution that satisfies simultaneously all equations of the Korteweg-de Vries
hierarchy.
