1995/09/25 by R. A. Kraenkel, M. A. Manna, Kraenkel, R. A. +5
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Advanced Mathematical Physics Problems
paper · pdf · doi:10.48550/arxiv.patt-sol/9509001
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.