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Extended shallow water wave equations

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Theodoros P. Horikis, Dimitrios J. Frantzeskakis, Noel F. Smyth

Fluid Dynamics · Submitted 10 May 2022

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

The authors' main claim Extended shallow water wave equations are derived, using the method of asymptotic expansions, from the Euler (or water wave) equations.

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arXiv ID2205.04884 (version 1)
Pith IDZGQPX72H, Pith's permanent record of this paper and its review
CitationDimitrios J. Frantzeskakis, Noel F. Smyth, Theodoros P. Horikis. "Extended shallow water wave equations." arXiv:2205.04884 (2022). https://pith.science/paper/ZGQPX72H
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,666 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.40 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Extended shallow water wave equations are derived, using the method of asymptotic expansions, from the Euler (or water wave) equations. These extended models are valid one order beyond the usual weakly nonlinear, long wave approximation, incorporating all appropriate dispersive and nonlinear terms. Specifically, first we derive the extended Korteweg-de Vries (KdV) equation, and then proceed with the extended Benjamin-Bona-Mahony and the extended Camassa-Holm equations in (1+1)-dimensions, the extended cylindrical KdV equation in the quasi-one dimensional setting, as well as the extended Kadomtsev-Petviashvili and its cylindrical counterpart in (2+1)-dimensions. We conclude with the case of the extended Green-Naghdi equations.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Extended shallow water wave equations are derived, using the method of asymptotic expansions, from the Euler (or water wave) equations. contribution 0.88 0.93 0.13 asserted 1.00
s1 These extended models are valid one order beyond the usual weakly nonlinear, long wave approximation, incorporating all appropriate dispersive and nonlinear terms. contribution 0.44 0.69 0.21 asserted 1.00
s2 Specifically, first we derive the extended Korteweg-de Vries (KdV) equation, and then proceed with the extended Benjamin-Bona-Mahony and the extended Camassa-Holm equations in (1+1)-dimensions, the extended cylindrical KdV equation in the quasi-one dimensional setting, as well as the extended Kadomtsev-Petviashvili and its cylindrical counterpart in (2+1)-dimensions. contribution 0.85 0.94 0.15 asserted 1.00
s3 We conclude with the case of the extended Green-Naghdi equations. contribution 0.86 0.87 0.33 asserted 0.87

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original abstract

Extended shallow water wave equations are derived, using the method of asymptotic expansions, from the Euler (or water wave) equations. These extended models are valid one order beyond the usual weakly nonlinear, long wave approximation, incorporating all appropriate dispersive and nonlinear terms. Specifically, first we derive the extended Korteweg-de Vries (KdV) equation, and then proceed with the extended Benjamin-Bona-Mahony and the extended Camassa-Holm equations in (1+1)-dimensions, the extended cylindrical KdV equation in the quasi-one dimensional setting, as well as the extended Kadomtsev-Petviashvili and its cylindrical counterpart in (2+1)-dimensions. We conclude with the case of the extended Green-Naghdi equations.

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