Kraenkel, Roberto André [UNESP]Manna, M. A.Merle, V.Montero, J. C. [UNESP]Pereira, J. G. [UNESP]2014-05-272014-05-271996-12-01Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, v. 54, n. 3, p. 2976-2981, 1996.1063-651Xhttp://hdl.handle.net/11449/64912By considering the long-wavelength limit of the regularized long wave (RLW) equation, we study its multiple-time higher-order evolution equations. As a first result, the equations of the Korteweg-de Vries hierarchy are shown to play a crucial role in providing a secularity-free perturbation theory in the specific case of a solitary-wave solution. Then, as a consequence, we show that the related perturbative series can be summed and gives exactly the solitary-wave solution of the RLW equation. Finally, some comments and considerations are made on the N-soliton solution, as well as on the limitations of applicability of the multiple-scale method in obtaining uniform perturbative series.2976-2981engArtigo10.1103/PhysRevE.54.2976WOS:A1996VK26500106Acesso restrito2-s2.0-02423446902-s2.0-0242344690.pdf1599966126072450