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- Multiple-time higher-order perturbation analysis of the regularized long-wavelength equation
- Universidade Estadual Paulista (UNESP)
- Université de Montpellier II
- By 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.
- Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, v. 54, n. 3, p. 2976-2981, 1996.
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