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The Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation

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R. A. Kraenkel, M. A. Manna, J. C. Montero, J. G. Pereira

patt-sol · Submitted 25 Sep 1995

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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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arXiv IDpatt-sol/9509001 (version 2)
Pith IDGVVMZ6HS, Pith's permanent record of this paper and its review
CitationJ. C. Montero, J. G. Pereira, M. A. Manna, R. A. Kraenkel. "The Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation." arXiv:patt-sol/9509001 (1995). https://pith.science/paper/GVVMZ6HS
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,387 input tokens.

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arXiv listing abstract v2. Results and the main claim are underlined; .

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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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. method 0.87 0.93 0.04 asserted 0.89
s1 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. result 0.99 0.91 0.89 asserted 1.00

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Original 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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