dorsal/arxiv
View SchemaThe Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation
| Authors | R. A. Kraenkel, M. A. Manna, J. C. Montero, J. G. Pereira |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9509001 |
| URL | https://arxiv.org/abs/patt-sol/9509001 |
Abstract
We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a secularity-free perturbation theory, we show that the well known N-soliton dynamics of the shallow water wave equation, in the particular case of $\alpha=2 \beta$, can be reduced to the N-soliton solution that satisfies simultaneously all equations of the Korteweg-de Vries hierarchy.
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"date_created": "2026-03-02T18:00:29.430000Z",
"date_modified": "2026-03-02T18:00:29.430000Z",
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"abstract": "We apply a multiple-time version of the reductive perturbation method to\nstudy long waves as governed by the shallow water wave model equation. As a\nconsequence of the requirement of a secularity-free perturbation theory, we\nshow that the well known N-soliton dynamics of the shallow water wave equation,\nin the particular case of $\\alpha=2 \\beta$, can be reduced to the N-soliton\nsolution that satisfies simultaneously all equations of the Korteweg-de Vries\nhierarchy.",
"arxiv_id": "patt-sol/9509001",
"authors": [
"R. A. Kraenkel",
"M. A. Manna",
"J. C. Montero",
"J. G. Pereira"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"title": "The Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation",
"url": "https://arxiv.org/abs/patt-sol/9509001"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "712f0012-77ba-45aa-b538-eb109d53f875",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
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