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

R. A. Kraenkel, M. A. Manna, J. C. Montero, J. G. Pereira

patt-solarXiv:patt-sol/9509001

Abstract

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=2 β, can be reduced to the N-soliton solution that satisfies simultaneously all equations of the Korteweg-de Vries hierarchy.

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