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

The Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation