dorsal/arxiv
View SchemaReductive Perturbation Method, Multiple-Time Solutions and the KdV Hierarchy
| Authors | R. A. Kraenkel, M. A. Manna, J. C. Montero, J. G. Pereira |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9509003 |
| URL | https://arxiv.org/abs/patt-sol/9509003 |
Abstract
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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"date_created": "2026-03-02T18:00:29.427000Z",
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"abstract": "We apply a multiple-time version of the reductive perturbation method to\nstudy long waves as governed by the Boussinesq model equation. By requiring the\nabsence of secular producing terms in each order of the perturbative scheme, we\nshow that the solitary-wave of the Boussinesq equation can be written as a\nsolitary-wave satisfying simultaneously all equations of the KdV hierarchy,\neach one in a different slow time variable. We also show that the conditions\nfor eliminating the secularities are such that they make the perturbation\ntheory compatible with the linear theory coming from the Boussinesq equation.",
"arxiv_id": "patt-sol/9509003",
"authors": [
"R. A. Kraenkel",
"M. A. Manna",
"J. C. Montero",
"J. G. Pereira"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"title": "Reductive Perturbation Method, Multiple-Time Solutions and the KdV Hierarchy",
"url": "https://arxiv.org/abs/patt-sol/9509003"
},
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"source": {
"execution_id": "3d3556c3-38d2-4965-8dd6-f7d829fad751",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
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