  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.
