Multiple-Time Higher-Order Perturbation Analysis of the Regularized   Long-Wavelength Equation
  By considering the long-wave 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. 
R.A. Kraenkel, M.A. Manna, V. Merle, J.C. Montero and J.G. Pereira