Kraenkel, Roberto André [UNESP]Manna, Miguel A.Montero, Juan C. [UNESP]Pereira, José G. [UNESP]2014-05-272014-05-271997-05-01Journal of the Physical Society of Japan, v. 66, n. 5, p. 1277-1281, 1997.0031-9015http://hdl.handle.net/11449/65097We 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.1277-1281engKdV hierarchyPerturbation theorySecularityArtigo10.1143/JPSJ.66.1277WOS:A1997XB37900013Acesso restrito2-s2.0-0031481541