Reductive Perturbation Method, Multiple-Time Solutions and the KdV Hierarchy

Details Reductive Perturbation Method, Multiple-Time Solutions and the KdV Hierarchy Reductive Perturbation Method, Multiple-Time Solutions and the KdV Hierarchy

1995-09-25

arxiv.org/abs/patt-sol/9509003v1

Nonlinear Sciences

Pattern Formation and Solitons

11 pages, RevTex, to appear in the proceedings of the workshop "Nonlinear Physics: Theory and Experiment", Gallipoli, Italy, J

Scientific paper

We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the Boussinesq model equation. By requiring the absence of secular producing terms in each order of the perturbative scheme, we show that the solitary-wave of the Boussinesq equation can be written as a solitary-wave satisfying simultaneously all equations of the KdV hierarchy, each one in a different slow time variable. We also show that the conditions for eliminating the secularities are such that they make the perturbation theory compatible with the linear theory coming from the Boussinesq equation.

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