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

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.

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

References in corpus (2)

• The Korteweg-de Vries Hierarchy and Long Water-Waves
• Boussinesq Solitary-Wave as a Multiple-Time Solution of the Korteweg-de Vries Hierarchy

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• Linearizability of the Perturbed Burgers Equation
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• Modified Korteweg-de Vries Hierachies in Multiple-Times Variables and the Solutions of Modified Boussinesq Equations
• Two-component description of dynamical systems that can be approximated by solitons: The case of the ion acoustic wave equations of Plasma Physics
• Perturbative analysis of wave interactions in nonlinear systems