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Initial boundary value problem for Korteweg-de Vries equation: a review and open problems

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Roberto de A. Capistrano-Filho (UFPE), Shu-Ming Sun (VT), Bing-Yu Zhang (UC)

Analysis of PDEs · Submitted 4 Oct 2018

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

The authors' main claim In this note we present a review of the main results about this topic and also introduce interesting open problems which still requires attention from the mathematical point of view.

how it is stated · asserted 0.97 read the record →

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arXiv ID1810.02698 (version 2)
Pith IDCG7XVQWL, Pith's permanent record of this paper and its review
CitationBing-Yu Zhang (UC), Roberto de A. Capistrano-Filho (UFPE), Shu-Ming Sun (VT). "Initial boundary value problem for Korteweg-de Vries equation: a review and open problems." arXiv:1810.02698 (2018). https://pith.science/paper/CG7XVQWL
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,283 input tokens.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In the last 40 years the study of initial boundary value problem for the Korteweg-de Vries equation has had the attention of researchers from various research fields. In this note we present a review of the main results about this topic and also introduce interesting open problems which still requires attention from the mathematical point of view.

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 the last 40 years the study of initial boundary value problem for the Korteweg-de Vries equation has had the attention of researchers from various research fields. background 1.00 0.04 0.04 asserted 1.00
s1 In this note we present a review of the main results about this topic and also introduce interesting open problems which still requires attention from the mathematical point of view. contribution 0.98 0.79 0.28 asserted 0.97

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 1.00.

What was examined, and what was not

sources read
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not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • T body sentences
  • C citations
  • R cross-paper relations

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 the last 40 years the study of initial boundary value problem for the Korteweg-de Vries equation has had the attention of researchers from various research fields. In this note we present a review of the main results about this topic and also introduce interesting open problems which still requires attention from the mathematical point of view.

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What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites

Cites as background 1 paper
  • The equation ([ref]) is called the Korteweg-de Vries equation in the literature, often abbreviated as the KdV equation, although it had appeared explicitly in Boussinesq’s massive 1877 Memoir [ref] , as equation (283bis) in a footnote on page 360[The interested readers are referred to [ref] for history and origins of the Korteweg-de Vries equation.].

    On the origin of the Korteweg-de Vries equation · Introduction · 0.95

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