MULTIPLE-TIME HIGHER-ORDER PERTURBATION ANALYSIS OF THE REGULARIZED LONG-WAVELENGTH EQUATION

By considering the long-wavelength limit of the regularized long wave (RLW) equation, we study its multiple-time higher-order evolution equa tions. As a first result, the equations of the Korteweg-de Vries hiera rchy are shown to play a crucial role in providing a secularity-free p erturbation theory in the specific case of a solitary-wave solution. T hen, as a consequence, we shaw that the related perturbative series ca n be summed and gives exactly the solitary-wave solution of the RLW eq uation. Finally, some comments and considerations are made on the N-so liton solution, as well as on the Limitations of applicability of the multiple-scale method in obtaining uniform perturbative series.