Multiple-Time Higher-Order Perturbation Analysis of the Regularized Long-Wavelength Equation
patt-sol
2009-10-30 v1 Pattern Formation and Solitons
Abstract
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.
Keywords
Cite
@article{arxiv.patt-sol/9606006,
title = {Multiple-Time Higher-Order Perturbation Analysis of the Regularized Long-Wavelength Equation},
author = {R. A. Kraenkel and M. A. Manna and V. Merle and J. C. Montero and J. G. Pereira},
journal= {arXiv preprint arXiv:patt-sol/9606006},
year = {2009}
}
Comments
15 pages, RevTex, no figures (to appear in Phys. Rev. E)