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The KP approximation under a weak Coriolis forcing

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Benjamin Melinand

Analysis of PDEs · Submitted 25 Oct 2017

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

The authors' main claim This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.

how it is stated · asserted 1.00 read the record →

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arXiv ID1710.09717 (version 3)
Pith IDMI56IPK7, Pith's permanent record of this paper and its review
CitationBenjamin Melinand. "The KP approximation under a weak Coriolis forcing." arXiv:1710.09717 (2017). https://pith.science/paper/MI56IPK7
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,849 input tokens.

What the abstract itself states, as probabilities: claims first 0.96 · states limitation 0.40 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.26 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq-Coriolis equations in this setting and we provide a rigorous justification of this model. Then, from these equations, we derive two other asymptotic models. When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev-Petviashvili equation (also called Grimshaw-Melville equation). When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev-Petviashvili equation. This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. contribution 0.78 0.82 0.06 asserted 0.76
s1 We derive the Boussinesq-Coriolis equations in this setting and we provide a rigorous justification of this model. contribution 0.83 0.96 0.12 asserted 1.00
s2 Then, from these equations, we derive two other asymptotic models. contribution 0.52 0.95 0.06 asserted 1.00
s3 When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev-Petviashvili equation (also called Grimshaw-Melville equation). result 0.82 0.93 0.29 asserted 1.00
s4 When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev-Petviashvili equation. result 0.84 0.94 0.22 asserted 1.00
s5 This work provides the first mathematical justification of the KP approximation under a Coriolis forcing. contribution 0.78 0.92 0.74 asserted 1.00

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

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq-Coriolis equations in this setting and we provide a rigorous justification of this model. Then, from these equations, we derive two other asymptotic models. When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev-Petviashvili equation (also called Grimshaw-Melville equation). When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev-Petviashvili equation. This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.

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