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Stability of KdV solitons on the half-line

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Márcio Cavalcante, Claudio Muñoz

Analysis of PDEs · Submitted 9 Jul 2017

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

The authors' main claim However, we are able to show that solitons placed initially far away from the origin are strongly stable for the problem posed on the right half-line, assuming homogeneous boundary conditions.

how it is stated · asserted 1.00 read the record →

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arXiv ID1707.02608 (version 2)
Pith IDHYGMP2TU, Pith's permanent record of this paper and its review
CitationClaudio Mu\~noz, M\'arcio Cavalcante. "Stability of KdV solitons on the half-line." arXiv:1707.02608 (2017). https://pith.science/paper/HYGMP2TU
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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, 4,886 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.91 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.40 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper we study the stability problem for KdV solitons on the left and right half-line. Unlike standard KdV, these are not exact solutions to the equations posed in the half-line. However, we are able to show that solitons placed initially far away from the origin are strongly stable for the problem posed on the right half-line, assuming homogeneous boundary conditions. For the problem posed on the left half-line, the positive infinitetime stability problem makes no sense for the case of KdV solitons, but in this setting we prove a result of stability for all negative times. The proof involves the use of almost conserved quantities adapted to the evolution of the KdV soliton on the particular case of the half-line. Adaptations to other boundary conditions or star graphs are also discussed.

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 stability problem for KdV solitons on the left and right half-line. contribution 0.78 0.80 0.05 asserted 0.71
s1 Unlike standard KdV, these are not exact solutions to the equations posed in the half-line. background 0.88 0.18 0.03 asserted 1.00
s2 However, we are able to show that solitons placed initially far away from the origin are strongly stable for the problem posed on the right half-line, assuming homogeneous boundary conditions. result 1.00 0.95 0.44 asserted 1.00
s3 For the problem posed on the left half-line, the positive infinitetime stability problem makes no sense for the case of KdV solitons, but in this setting we prove a result of stability for all negative times. result 0.96 0.94 0.17 asserted 1.00
s4 The proof involves the use of almost conserved quantities adapted to the evolution of the KdV soliton on the particular case of the half-line. method 1.00 0.90 0.04 asserted 0.97
s5 Adaptations to other boundary conditions or star graphs are also discussed. contribution 0.64 0.68 0.03 asserted 0.83

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 stability problem for KdV solitons on the left and right half-line. Unlike standard KdV, these are not exact solutions to the equations posed in the half-line. However, we are able to show that solitons placed initially far away from the origin are strongly stable for the problem posed on the right half-line, assuming homogeneous boundary conditions. For the problem posed on the left half-line, the positive infinitetime stability problem makes no sense for the case of KdV solitons, but in this setting we prove a result of stability for all negative times. The proof involves the use of almost conserved quantities adapted to the evolution of the KdV soliton on the particular case of the half-line. Adaptations to other boundary conditions or star graphs are also discussed.

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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 · 3 sentences without a confident label

Uses the method or tool of 1 paper
  • By direct application the ideas used in [ref] and [ref] we believe that the following two boundary conditions [equation] [equation] are sufficient to ensure local well-posedness.

    The Korteweg-de Vries equation on a metric star graph · Comments on the KdV equation on graphs · 0.83

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