The Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation - Kraenkel, Roberto André [UNESP]; Manna, Miguel A.; Montero, Juan C. [UNESP]; Pereira, José G. [UNESP] (Physical Society of Japan, 1997)
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 α = 2β, can be reduced to the N-soliton solution that satisfies simultaneously all equations of the Korteweg-de Vries hierarchy.
Keywords: KdV hierarchy; Perturbation theory; Secularity