Multiple-Time Higher-Order Perturbation Analysis of the Regularized Long-Wavelength Equation

Details Multiple-Time Higher-Order Perturbation Analysis of the Regularized Long-Wavelength Equation Multiple-Time Higher-Order Perturbation Analysis of the Regularized Long-Wavelength Equation

1996-06-27

arxiv.org/abs/patt-sol/9606006v1

Nonlinear Sciences

Pattern Formation and Solitons

15 pages, RevTex, no figures (to appear in Phys. Rev. E)

Scientific paper

10.1103/PhysRevE.54.2976

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.

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