Kraenkel, Roberto André [UNESP]Manna, M. A.Pereira, J. G. [UNESP]2014-05-272014-05-271995-12-01Journal of Mathematical Physics, v. 36, n. 1, p. 307-320, 1995.0022-2488http://hdl.handle.net/11449/64670By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the requirements of scale invariance and absence of secular terms in each order of the perturbative expansion, we show that the Korteweg-de Vries hierarchy equations do play a role in the description of such waves. Finally, we show that this procedure of eliminating secularities is closely related to the renormalization technique introduced by Kodama and Taniuti. © 1995 American Institute of Physics.307-320engArtigo10.1063/1.531294WOS:A1995QA69400019Acesso aberto2-s2.0-218445212622-s2.0-21844521262.pdf1599966126072450